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COPYRIGHT DEPOSIT: 



A Practical Course in 
Mechanical Drawing 

For Individual Study and Shop Classes, 
Trade and High Schools 



BY 

WILLIAM F.WILLARD 

FORMERLY INSTRUCTOR IN MECHANICAL DRAWING AT THE 
ARMOUR INSTITUTE OF TECHNOLOGY 



With 157 Illustrations, a Reference Vocabulary 
and Definitions of Symbols 



CHICAGO 

POPULAR MECHANICS COMPANY 

PUBLISHERS 





1 ■i>5'^ 


• 


.w^^ 




Copyright, 1912 






By 






H. H. WINDSOR 




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V 





€CI.A305934 



CONTENTS 



CHAPTER I 
Introductory 7 

CHAPTER n 
The Draftsman's Equipment n 

CHAPTER HI 
Geometric Exercises with Instruments 17 

CHAPTER IV 
Working Drawings 58 

CHAPTER V 
Conventions Used in Drafting 70 

CHAPTER VI 
Modified Positions of the Object 77 

CHAPTER VII 
The Detailed Working Drawing 81 

CHAPTER VIII 
Pattern-Workshop Drawings 92 

CHAPTER IX 
Penetrations no 

CHAPTER X 
The Isometric Working Drawing 121 

CHAPTER XI 
Miscellaneous Exercises , 126 

CHAPTER XII 
A Suggested Course for High Schools 156 



REFERENCE VOCABULARY 

FOR the benefit of those who, for the first time, may meet 
new terms and expressions in this manual the following 
vocabulary, with definitions, is appended: 

Altitude. Vertical height. 

Angle. Space between two intersecting lines. 

Apex. Point where converging lines meet. 

Apices. More than one apex. 

Arc. Any part of the circumference of a circle. 

Area. Surface in units of measurement. 

Bisect. To cut in two equal parts. 

Bisector. A line which bisects. 

Chord. The line connecting any two points of an arc of a 
circle. 

Circumference. The boundary of a circle. 

Circumscribe. To draw around. 

Convention. Customary method or symbol used in pro- 
ducing a drawing. 

Decagon. Figure of ten sides and ten angles. 

Degree. One 360th part of a circle. 

Diameter. The distance measured across the center of a 
circle or a line drawn through the center terminating in the 
circumference. 

Element. A part which goes to make up the whole. 

Elevation. A view of an object looking at the front or side. 

Elliptical. Pertaining to the shape of an ellipse. 

Equilateral. Equal-sided. 

Frustum. Remaining portion of a cone or pyramid when 
the top has been removed parallel to the base. 

Hemisphere. Half a sphere. 

Heptagon. Figure of seven sides and seven angles. 

Hexagon. Figure of six sides and six angles. 

Horizontal. Parallel to the horizon. 

Hypotenuse (spelled also Hypothenuse). The diagonal 
distance between opposite angles of a rectangle or the side 
opposite the right angle. 

Isometric. Of equal measurement. 

Isosceles Triangle. A triangle with two sides of equal 
length and base angles equal. 
Lateral. Side. 

IV 



REFERENCE VOCABULARY 

Line. That which has length only. 

Median. Line drawn from the vertex of an angle to the 
middle point of the opposite side of a triangle. 

Nonagon. Figure of nine sides and nine angles. 

Octagon. Figure of eight sides and eight angles. 

Orthographic. Derived from two Greek words, orthos. 
straight and graph, to write. Hence applied to a straight-line 
drawing determined by projection on H, V and P. 

Parallel. Lines or planes are said to be parallel when all 
ooints of one are equally distant from all points of another. 

Parallelogram. A four-sided figure with opposite sides par- 
allel and of equal length. 

Pentagon. Figure of five sides and five angles. 

Perimeter. The distance measured around. 

Perpendicular. Any line at right angles to another. 

Pi (tt). a Greek letter used as a convenient symbol to 
express the relation between diameter and circumference, tt 
— 3.1416. The diameter of a circle X "^ = circumference. 

Plan. A view looking down upon the top. 

Plane. A surface with length and width and no thickness. 

Plinth. A prism whose height is less than any one of its 
other dimensions. 

Point. That which has position only. 

Polygon. A plane figure bounded by four or more sides. 

Prism. A figure bounded by rectangular faces, two of which 
are parallel. 

Project. To point toward. 

Pyramid. A solid with triangular faces converging to a 
common vertex. 

Quadrant. The fourth part of a circle. 

Quadrilateral. A four-sided polygon. 

Radius. Half the diameter. 

Radii. The plural form of radius. 

Rectangle. A plane figure with four right angles of 90° 
each. 

Rectify. To make straight or right. 

Rectilinear. Pertaining to right or straight lines. 

Rotate. To roll. 
^ 'Scalene Triangle. A triangle all sides of which are unequal 
in length. 

Section. A view determined by a cutting plane. 

V 



REFERENCE VOCABULARY 

Sector. A radial division of a circle or the space between 
two radial elements. 

Segment. The space between the chord and arc of a circle. 

Semi-circle. Half a circle. 

Sphere. Ball or globe. A solid with all points of the 
surface equally distant from a point within, called the center. 

Tangent. To lie adjacent at a single point. 

Triangle. A three-sided figure. 

Trisect. To cut into three equal parts. 

Truncate. To cut off. 

Vertex. A common point of several converging lines. 

Vertical. Always straight "up and down." 



DEFINITIONS OF SYMBOLS 

27rR Circumference of a circle when R — radius. 
7rR2 Area of a circle when R = radius. 
1 Perpendicular. 
II Parallel. 

= Means "equals'" or "is equal to". 
A. Angles. 

X Intersecting, or multiplied by, as the case may be. 
.". Therefore. 

L Right angle. Two intersecting lines making 90° to each 
other. 

Z Acute angle. Two intersecting lines less than 90° to each 
other. 

^^"^ — Obtuse angle. Two intersecting lines more than 90° to 
each other. 

H Horizontal. 

V Vertical. 

P Profile. 

GL Ground line. 

VL Vertical line. 



VI 



PRACTICAL MECHANICAL 
DRAWING 

CHAPTER I 

INTRODUCTION 

IV/TECHANICAL drawing is one of the most popular 
^^^ and most profitable subjects of study for the boy 
or young man of today. It is an essential qualification 
in most lines of engineering, an almost indispensable 
accomplishment in many occupations, and often the 
secret of successful advancement. It is founded upon 
the science of geometry, which, as applied to drawing, 
becomes a delightful and interesting subject, and not 
the difficult study the beginner fears. For illustration, 
a farmer wishes to know how many gallons of water 
will fill a tank, the diameter and height being known ; 
how many bushels of wheat will fill a bin, or how many 
acres there are in a field a quarter of a mile square. 
These examples, like many others, illustrate the prac- 
tical application of geometry, a subject no less impor- 
tant to the mechanic than the farmer, but a thousand 
times more interesting to the student than the usual 
text book. 

In preparing this manual the author was ever mind- 
ful of the many circumstances and limitations which 
have so often combined to deny to aspiring youth the 
advantages of a complete education. In this day and 
age competition and industrial conditions demand the 
best training and skill for every productive effort. 
What the artisan or mechanic does to improve himself 



8 A PRACTICAL COURSE IN 

intellectually, to this end, increases his efficiency and 
value to his employer in every respect. 

In geometry a student is concerned with the theorem 
of a problem, and the proof, or why it is so. In me- 
chanical drawing the mechanical operations of con- 
struction — the actual doing of a problem, graphically, 
by the use of compass, triangles and other instruments 
— is considered essential and sufficient. However, this 
course does not preclude a master's knowledge of the 
principles of geometry. Any live, wide-awake boy can 
apply, to a good advantage, these geometric exercises 
to some project which he desires to work out or invent, 
without first having studied the subject. 

The surveyor with his tape and transit, the architect 
or mechanical engineer with his slide rules and for- 
mulas, must know these exercises also. If a craftsman 
desires a brace or bracket for a plate rail, he must know 
how to 'iay out'' the desired curves and angles. If a 
boy desires to make a taboret or jardiniere-stand with a 
hexagonal or octagonal top, he must first solve the geo- 
metric problem or consequently be unhappy with the 
results. 

One reason for not accepting a freehand perspective 
sketch as a substitute for the geometric drawing lies in 
the fact that the sketch seldom shows all the informa- 
tion required for the workman. The sketch deals with 
outward appearances only and from one viewpoint. 
The mechanical drawing of an object delineates the 
actual facts, within or without, and from as many view- 
points as the object has dimensions. Any hidden or de- 
tailed information is considered as important as that 
which is visible, and these details are represented ac- 
cordingl}^ by suitable conventions, the word convention. 



MECHANICAL DRAWING 9 

in drafting, meaning a customary symbol or m.ethod 
established by precedent. 

The freehand sketch is governed by well-known 
laws of perspective which constitute the language of 
the artist from the esthetic standpoint. The mechan- 
ical drawing is represented by customary shop and 
drafting-room conventions and is the language of the 
mechanic and artisan. The one develops the power of 
observation, good judgment and individuality; the 
other, precision, accuracy and mechanical ability. 

An advantage that the mechanical drawing has over 
the sketch is that the workman will not be apt to con- 
fuse apparent dimensions, as seen from the perspect- 
ive, with true measurements, as seen from the work- 
man's drawing. All working drawings are made to 
scale, and all dimensions are proportional and properly 
placed. They must be made in such a manner that 
the ''dumbest" man in the shop will understand them. 
Otherwise, if an error occurs in construction, the blame 
attaches to the draftsman. Such a drawing must keep 
in mind all those who must, of necessity, use it. Me- 
chanics, designers, engineers and artisans of any trade 
fully realize the importance of a definite plan of pro- 
cedure. Bridges, buildings, railroads and canals must 
be thought out on paper, and their feasibility satis- 
factorily passed upon, before a mechanic or construc- 
tion company begins the actual work. Perhaps the 
most important part, if not the most difficult, is the 
making of the plans and specifications. The next most 
important part is working according to the direction of 
the plans. 

^Constructive drawing also finds expression in a mul- 
titude of shops. A cabinetmaker, machinist, pattern- 
maker, or contractor, must have intelligent pictures or 



10 MECHANICAL DRAWING 

drawings to guide his hands, and these drawings must 
be accurate and clear. A draftsman, whether amateur 
or professional, who fails to make them so, may, 
through ignorance and carelessness, or both, cause a loss 
of great consequence to his employer and the world at 
large. Someone has said : ''Mechanical drawing is the 
alphabet of the engineer ; without it he is only a hand. 
With it he indicates the possession of a head.'' It is 
needless to say that the hand will only do what the 
head directs. 

A uniform code of conventions and symbols is re- 
quired among workmen and shops just as among tele- 
graph operators. Such a language, if it may be so 
called, has come to be accepted generally among drafts- 
men who adhere closely to the modern approved forms, 
and these will be used throughout this manual 



CHAPTER II 

THE draftsman's EQUIPMENT. 

'T^HE old saying that a poor workman blames his 
^ tools is very nearly if not always true, for if a 
workman is content to work with an instrument poor 
in quality or poorly kept, it must be taken that he ex- 
pects to do poor work. How can a draftsman produce 
an accurate drawing if the compass legs are not firm 
and the points blunt, T square nicked, triangles warped, 
pencil dull, ruling-pen clogged with ink, and many 
other possible imperfections which would mar the 
finished drawing? Hence, it goes without saying that 
to do commendable work one must have good mate- 
rials, take excellent care of them and keep them in per- 
fect repair. A complete list is appended below, though 
not all are required. Those marked with stars are 
essential ; the others are luxuries : 

"^Drawing-Board — 16x21 in., inlaid, can be made of 
A No. I soft white pine by mortising narrow strips 
across each end of the board. The size is not arbitrary. 
Local conditions may require smaller boards and thus, 
of course, smaller plates. Fig. i. 

"^Drawing-Paper — Whatman's hot or cold-pressed 
(white) paper. Keufifel & Esser or E. Dietzgen 
cream paper, size 12x16 in. or 15x20 in.; but size of 
board and paper to be determined by local conditions, 
per above. A good bond paper may also be used. Two- 
ply bristol paper is excellent. For Patent Office draw- 
mgs three-ply bristol paper is required. 

"^Thumb-tacks — Comet No. 2 is one of many good 
tacks. They come in small tin cartons. 

n 



12 A PRACTICAL COURSE IN 

"^Pencils — 2H and 4H. Sharpen so that the lead is 
exposed jq or f in. 

"^Erasers — Faber No. 211, Art Gum, Eberhard 
typewriter ink eraser, or others as good. 

"^Scale — Ordinary hardwood rulers will do at first. 
A triangular boxwood scale, divided into different 
scales, is best. 

"^T Square — Should be as long as the board and made 
of pear wood. Boys can make this in the wood shop. 
Fig. I. 

"^Triangles — 30-60-90 celluloid, 8 in. or 10 in. long, 
45-90, celluloid, 6 or 8 in. long. Wooden triangles 
are inaccurate. Fig. i. 

Emery Pad — Or No. 000 sand-paper, to sharpen 
pencils. Each pencil should be sharpened chisel- 
shaped at one end and conical at the other. Use a 2H 
or 4H-grade. 

^French Curve — Celluloid. Lead curves are cum- 
bersome and expensive. 

Case or set of Instruments — Containing: 

*i compass with lead and pen adjustment and 
lengthening bar. 

I divider (large). 

I divider (bowspring) 3 in. long. 
*i ruHng-pen (large). 

I ruling-pen (small). 

I bowspring compass (ink). 

I bowspring compass (pencil). 

I box leads. 

1 protractor (German make preferable). 

I penholder and pen. No. 506 and No. 516, ball- 
pointed. 



MECHANICAL DRAWING 



13 



*i bottle Higgins' water-proof ink (black). 

1 typewriter erasing-shield (celluloid or nickel- 
plated). 

These instruments, including the paper, need not be 
expensive, f. e., those marked with stars. Cheap brass 
sets are worse than useless. If it is convenient, the 
purchaser should consult with a practical draftsman 
before selecting the materials. 




Case of Instruments 
HOW TO USE THE MATERIALS 

1. The paper should be tacked in the upper left- 
hand corner of the drawing-board so that the T square 
may not slip when drawing the lowest lines on the 
plate. 

2. Thumb-tacks should not be withdrawn by the 
fingers. Use a knife blade or other flat instrument. 

3. To get clean, sharp lines, pencils should be 
sharpened frequently, but under no circumstances must 
ridges be made on the drawing by heavy pressure on 
the pencil. 



14 A PRACTICAL COURSE IN 

4. Use a soft gum eraser to clean the drawing be- 
fore inking, that a glossy finish to black lines may be 
retained. Use ink-erasers for pencil lines only in ex- 
ceptional cases where the pencil has caused deep ridges 
in the paper. All division lines should be erased before 
inking. 

5. All dimensions should be stepped off from the 
scale or ruler, with dividers, and then pricked lightly 
in the required place on the drawing. Explanation will 
be given later as to how to scale a drawing properly. 

6. Always use the upper edge of the T square, 
which should be held against the left-hand edge of the 
drawing-board. Never use the upper edge of the square 
as a cutting edge. The least nick will cause inaccurate 
work as long as it is used thereafter. Fig. i. 

7. The triangles, which are used to draw oblique 
and perpendicular lines, should rest upon the upper 
edge of the T square. Many and various combina- 
tions of angles may easily be made by combining both 
the 30-60 and 45-90. The oblique side of the triangle 
should always be to the right while in use, whether in 
inking or penciling. Fig. i. 

8. The celluloid irregular curve is used in defining 
curves which are impossible to obtain with the compass. 
It is composed of many curves, but has seldom the 
right one, so that it is often necessary to shift it into 
many positions before required results may be ob- 
tained. 

9. Only tw^o instruments in the case need explana- 
tion, and this is better acquired by practice. The com- 
pass legs are jointed so that the nibs of the pen may be 
square to the surface of the paper while the circle is 
being drawn. The hand should describe the circle 
above the paper while in operation, and not remain sta- 



MECHANICAL DRAWING 



15 



tionary. The ruling-pen should incline slightly in the 
direction of the line and should be held so that the nibs 
of the pen are not in contact with the edge of the T 
square. To keep the instruments from corroding, 
polish them with a small chamois skin and five cents' 
worth of chalk precipitate, or Spanish whiting. Instru- 









Fier. 1 



ment must be kept clean. A thin piece of linen should 
be drawn between the nibs of the pen after each using, 
as the air congeals the ink quickly. The pen is filled 
by dropping the ink from the quill, — which is in the 
stopper of the bottle, — while being held in a vertical 
position. It should never be filled over one-quarter 
inch.' Lines are ruled from left to right and bottom 
upward. Use the adjusting screw to get the desired 
width. 



16 MECHANICAL DRAWING 

10. The German protractor is a semi-circular in- 
strument graduated into i8o degrees. This is used to 
obtain angles other than those obtained by the trian- 
gles. 

11. Higgins' inks are waterproof. Should a blot 
occur, first erase with the ink eraser. (Never use a 
knife.) Second, glaze the roughened surface by using 
the back of a bonehandled knife, or soapstone. Third. 
*'size'' the glazed surface by spreading over it a thin 
coat of graphite, from a soft pencil. The paper is now 
ready to re-ink. 



CHAPTER III 

GEOMETRIC EXERCISES WITH INSTRUMENTS 

T^ XERCISE I. — Bisect a line of any length and arc 
-'-^ of suitable radius. Construction: With radius 
greater than one-half of AB and points A and B as cen- 
ters describe intersecting arcs at i and 2. If a line be 
drawn from i to 2 it will bisect AB. Fig. 2. 




Fig. 2 



Exercise 2, — Erect a perpendicular to a given line 
(Problem i.) Fig. 2. Second method. Construction: 
From a given point E outside the given line AB draw a 
line at any angle to AB. Bisect and inscribe a circle 



17 



18 



A PRACTICAL COURSE IN 



about CD. Where the circle cuts AB is a point of the 
± through point E. Figs. 2 and 3. 

Exercise 3. — To draw a /^ line through a given point 
X to a given line AB. Construction : From any point 




Fig:. 3 

B on the given line and a radius equal to BX describe 
arc. From X and same radius describe a similar arc 
through B. Lay off BY on second arc = to AX. A 
line drawn through X and Y is ^ to AB. Fig. 4. 

Second method. Construction : Draw a line making 
any angle with AB. With C as center and any radius 




20 



A PRACTICAL COURSE IN 



describe an arc making angle 0. Duplicate this angle 
with given point as center. Fig. 4. 

Exercise 4. — Divide two lines into proportional parts. 
Construction : Lay off one line into any number of 
divisions. Connect the extremities of each line. By 
means of triangles draw parallels through remaining 
points. Fig. 5. 

Exercise 5. — Construct tangents to a given arc of 




Fig. 8 



any radius. Construction : With any radius describe 
arc of a circle. From the center of the arc to any point 
of the circumference draw^ a radial line. At the ex- 
tremity of the radial on the circumference erect a 1. 
This is the required tangent. Fig. 6. 

Exercise 6. — Duplicate and bisect a given angle. 
Construction: Draw any two intersecting lines, 
making any convenient angle. To duplicate, draw CD 
with any length. Describe an arc cutting given angle 
at A and E. With same radius describe arc cutting CD 
at F. Lay off, with F as center, the distance AE, and 
draw the other side of angle through C and G. Bisect 
as in Exercise i. Fig. 7. 



MECHANICAL DRAWING 



21 




Fig. 10 



22 A PRACTICAL COURSE IN 

Exercise 7. — To draw angle of 60°. Construction: 
With any line as a base and any point therein as a cen- 
ter, describe an arc of any convenient radius, cutting 
the base line at C. With C as a center and radius AC 
describe arc at E. A line through AE is 60° to xAB. 
Bisect to get angle of 30°. Other angles can be easily 
determined. 22^ 30^ reads 22 degrees and 30 minutes 
or 22y2 degrees. (Fig. 8.) The table is as follows: 

60" (seconds) = i minute (^). 
60^ (minutes) = i degree (°). 
360^ (degrees) = i circle. 

[Note the characters (' and ") used to designate 
minutes and seconds are used also to designate feet and 
inches. The context will, however, generally avoid 
confusion as to their meaning.] 

Can any angle be trisected ? 

Exercise 8. — By triangles only, divide a semicircle 
into angles of 15°. Use T square as a base for the tri- 
angles. Fig. 9. 

Exercise p. — Rectify a quadrant of a circle. Ap- 
proximate methods. Construction : Draw a circle of 
any suitable diameter and divide into quadrants. Draw 
a tangent of indefinite length at lower end of CD. 
Through A draw a line making 60° to this tangent. 
Where it cuts BD determines the length of the arc AD. 
Any smaller arc can be determined by extending^, 
through C and the other end of the given arc, a Hne to 
BD. Fig. 10. Second method. Approximate. Fig. 
II. AE = BD, Fig. 10. 

Exercise to. — Construct a right-angle triangle one 
angle of which is 30*^. The sum of all angles of any 
triangle is 180°. If a right angle is 90°, what must the 
remaining angles be ? This exercise is applicable as an 



MECHANICAL DRAWING 



23 



aid in determining the pitch or length of a rafter, when 
the rise and run are given. Pythagoras discovered the 
principle that the square of the rise + the square of the 
run equals the pitch squared : X^ -f Y^ =z Z^. Fig. 12. 




Fig. 11 



Exercise 11. — To find approximately the distance 
across an unknown area by means of similar right 
angles. Construction: Select a tree or object on the 
opposite bank or side as indicated at A. Select another 




Fig. 12 



on this side, say D. Lay off a convenient distance from 
D to C in the line ADC. Select a point B at right an- 
gles to AD and construct a parallelogram r)ODC. De- 
termine point X on the ground wdiich is in line with OC 



24 



A PRACTICAL COURSE IN 



and BA and measure the distance XO. By proportion, 

BDX BO 

AD : BD : : BO : XO .'. AD = 

XO 
Lay out the diagram, substituting known values for 
BD and DC and solve. Fig. 13. 




Exercise 12, — Equilateral triangle. Construction : 
Assume any length for a base. With a radius equal to 
the length of base and each terminal C and D as cen- 
ters describe intersection at X. Connect this point by 
lines to C and D. Measure the angles of an equilateral 
triangle in degrees. What is their sum ? Stained-glass 
windows are often laid out in Gothic arch forms by 
this kind of triangle. Fig. 14. 

Exercise 13. — Isosceles triangles. Construction : On 
a line of given or assumed lengths and with a radius 



MECHANICAL DRAWING 



25 




Fig. 14 



greater or smaller than AB proceed as in the problem 
above. Are all the angles equal? What is their sum? 
Fig. 15. 

Exercise 14. — The vertex angle of an isosceles tri- 
angle is 150°, and its base is 3 inches long. Without 
protractor make a drawing. The trilium is an early 




Fig. 15 



26 A PRACTICAL COURSE IN 

spring flower shaped on the order of an isosceles tri- 
angle. 

Exercise 13. — Scalene triangle. Base 2;^ inches, 
and base angles 22y2° and 37/4° respectively. What 
is the sum of the angles? Of any triangle? Fig. 16. 

Exercise 16. — Inscribe a square within a 3 inch 
circle. Without. Fig. 17. 

Exercise //. — Circumscribe a square about the circle 
in the problem above. What is the relation of inner to 




Fig. 16 

outer square? The syringa is a four-petaled flower 
shaped like a square. 

Exercise 18. — Pentagon within a circle. Construc- 
tion : Bisect the diameter of the circle. Bisect a ra- 
dius. With C as center and AC as radius, describe arc 
at B. With A as a center and AB as a radius, describe 
arc on the given circle at D. AD is the length of one 
side of the polygon. Lay off remaining sides and 
draw a star. Fig. 18. 

What is the size of an interior angle? Use pro- 
tractor. 



MECHANICAL DRAWING 



27 




Fig. 17 




Fig. 18 



28 



A PRACTICAL COURSE IN 



Exercise ip. — Pentagon. Construction: Base ij4-i5^- 
With one radius = to the base length describe arcs 
from centers i, 2 and 3. Connect i and 2 with 7 and 
8 and complete the pentagon. Inscribe a circle within 




Fig. 19 



the figure. Circumscribe a circle about the polygon. 
Many flower forms — pansy, violet — are pentagonal in 
shape. Fig. 19. 

Exercise 20. — Hexagon. Within a circle. Construc- 
tion : Lay off the radius six times on the circumfer- 
ence of the circle and connect the points. Without the 
protractor, what is the interior angle of this polygon ? 



MECHANICAL DRAWING 



29 



Use this key : 2n — 4 right angles when n = the num- 
ber of sides of the polygon. 

(2X6)— 4X90^ 



= 120^ 



n 



Prove this to be true. Draw a six-pointed star. Fig. 
20. 




Fi£:. 20 



Exercise 21* — Hexagon by means of the 30-60 tri- 
angle. The hexagonal bolt is an illustration of the use 
of the hexagon. Fig. 20. 



Exercise 22, — Hexagon without a given circle. 



Fig. 



21 



Exercise 2^. — Heptagon within a circle. Construc- 
tion. Draw a line making any angle with AB. Divide 
AB into as many equal divisions as the polygon 
has sides. With A and B as centers and AB as a radius 



30 














^^"'^'^^^ 




1 


/ 
\ 


\ 


^^^^30 






k. 




J 




Fig. 21 . 




A- 


t-r V / / / 


1 

/ 

1 
/ 

/ 


/ 

L>9 


1 


t 2\ 3 ^ 5 


6 

7 


7^ 






Fig. 22 


/ 





MFXHANICAL DRAWING 



31 



describe arcs at C. A line drawn through C and 2, 
cutting the circle at D, determines the length of one 
side of the heptagon. This method will apply to any 
polygon. Use above formula to determine the size of 
the interior angle. Fig. 22. 




Fig. 23 



Exercise 24. — Octagon within a circle. Construc- 
tion : Within a circle of an assumed diameter, divided 
into quadrants, draw bisectors. The circumference is 
now divided into eight equal divisions. Determine and 
locate the size of the interior angle by the preceding 
formula. Fig. 23. 

Exercise 2^. — Octagon within a square. Fig. 2^). 

Exercise 26. — Combination of polygons on a given 
base of i inch. Construction : Proceed as in laying 
out a hexagon. Bisect the arc A-2. Trisect 2-B. With 
center 2, draw arcs cutting through C and D at i and 3. 



32 A PRACTICAL COURSE IX 

Points I and 3 are centers of circles circumscribing 
polygons of the required number of sides. Fig. 24. 

Exercise 2J. — Inscribe circles about the triangles 
given in problems 10, 12, 13 and 15. 

Exercise 28. — Inscribe three circles in the triangle 
given in Problem 12. Construction: Draw the me- 
dians of each side or bisect each interior angle. Bisect 
angle AC. Where the bisector cuts the line OX is the 
center for one circle. Fig. 25. 

Exercise 2g. — Five circles tangent to a given circle 
and each other ; within or without the given circle. 
Construction : Divide the given circle into live equal 
parts and bisect each sector. The centers of each circle 
will be located on the bisector. Draw a tangent at the 
terminal of a bisector and extend it until it cuts a radial 
line. Bisect the angle this tangent makes with the ra- 
dial and extend this bisector until it cuts AB at C, 
which is the center of one circle. Fig. 26. 

Exercise 50. — A circle tangent to a given circle and 
a given line. Construction : With the radius of the 
required circle added to the radius of the given circle, 
and C as a center, strike an arc 1-2. Draw a line paral- 
lel to the given line with the distance = to the radius 
O of the required circle. WTiere this line and arc 1-2 
intersect is the center E for the required circle. 
Fig. 27. ^ 

Exercise 31. — A shaft i^ inches in diameter rotates 
within a ball-bearing consisting of 10 tempered steel 
balls. ]\Iake a drawing illustrating size of balls re- 
quired. Fig. 28. Approximate. Construction: Pro- 
ceed as in problem 29 except that the tangent circles are 
external to the given circle. 

Exercise ^2. — Four largest circles that can be drawn 
within a square. 



MECHANICAL DRAWING 



35 



Exercise JJ. — A Maltese cross. Fig. 29. Construc- 
tion : Draw two equal circles upon the two diameters 
of a given large circle and proceed as indicated in the 
drawing. 

Exercise 34, — Draw a geometric border using the 
circle as a unit. Nearly all design is geometric in char- 
acter. Fig. 30. 




Fig. 28 



Exercise 55. — Figure 31 is an original illustration 
of the Swastika. 

Exercise ^6. — Geometric monogram within a trefoil. 
Fig. 7,2, 

Exercise 57. — Moldings, i. Cyma Recta, Fig. 33. 
2. Roman Ogee, Fig. 34. 3. Scotia, Fig. 35. 4. 
Echinus, Fig. 36. Ogee Arch, Fig. 37. 



MECHANICAL DRAWING 39 

Exercise 38. — The astronomer tells us that the plane 
of the earth's orbit is called the "ecliptic." This is an 
ellipse in shape. Draw an ellipse by two methods. The 
upper half to be constructed as follows: AC=4j^ 
inches. DE = 354 inches. DM = AB. M and F are 
centers of all arcs on the ellipse. From C as center lay 
off on BC any number of points, i, 2, 3, 4, 5, etc. With 
C-i as a radius and M and F as centers describe arcs. 




Figr, 37 

With A-i as a radius and MF as centers describe arcs 
intersecting C-i. These are points of the eUipse. Pro- 
ceed until enough points are determined to locate the 
curve. 

The lower half by the circle method is self-evident 
from the illustration. Fig. 38. 

Exercise jp. — Trammel method. Fig. 39, Con- 
struction : Lay oft* on a small strip of cardboard the 
semi-minor and semi-major axes equal to the dimen- 
sions of the above problem. Move the point C so that 
it is always on the line AB and the point E on DF. By 



40 



A PRACTICAL COURSE IN 




Figf. 38 




Fig. 39 



MECHANICAL DRAWING 



41 



changing the position of the trammel frequently, suf- 
ficient points can be located at G, on the trammel, to 
determine a symmetric ellipse. Make GC = DH and 
GE = AH. 

Exercise ^o.— Make a full-size drawing of the ellip- 
tic cam. Fig. 40. 




Exercise 41. — A point on a connecting rod of a sta- 
tionary engine describes an elliptic curve in one revo- 
lution of the crank wheel. With B as the given point 
lay out the desired curve. The construction for the 
mechanism m.ay be omitted. Fig. 41. 

Exercise 42, — Five-point elliptic arch with three 
radii. Construction: AB, the altitude, and CD, the 
span, are given. Lay off the major and semi-minor 



MECHANICAL DRAWING 



43 



axes. With A as a center and AB as a radius, draw 
an arc through BE. Bisect CE at F and describe an 
arc with CF as radius. CG = AB and is 1 to CD. 
G-3 is 1 to BC, and where G-3 intersects CD at i is a 
point of the first center of the elHpse. Where it cuts 
AB at 3 is another. Make AH=BK. With 3 as a 
center and 3-H as a radius describe an arc through H. 
With C as a center and AK as a radius strike an arc at 




Fig. 43 



N. With I as a center and i-N as a radius strike arc 
at 2, which is another point of a center for the elHpse. 
With the construction duphcated on the right of the 
illustration the remaining centers are determined. 
Points I, 2, 3, 4 and 5 are the required centers, and all 
arcs and facing stones radiate from their respective 
centers. Fig. 42. 

Exercise 43. — Cycloid. Fig. 43. A curve generated 
by the motion of a point on the circumference of a 
circle which rolls on a straight line is called a cycloid. 
The figure clearly illustrates the construction. Im- 
agine the rolling circle to be the end of a cylinder. 

Exercise 44. — Epicycloid. Fig. 44. An epicycloidai 
curve is generated by the motion of a point on the cir- 
cumference of a circle which rolls upon a circle. 

Exercise 43. — Hypocycloid. Fig. 45. A hypocy- 
cloidal curve is generated by the motion of a point on 



44 



A PRACTICAL COURSE IN 




Fig. 44 

the circumference of a circle rolling upon the concave 
side of a circle. Should the diameter of the generating 
circle = the radius of the larger circle the hypocy- 
cloid would become a straight line. 

These curves are used in constructing the profile of 
gear teeth. Fig. 46 is a draftsman's method of laying 
out the forms of teeth theoretically, the method to the 
right being involute, and that to the left, cycloidal. Fig. 
46a is a perspective sketch of the same from a pattern 
made by a patternmaker in the shop. The size of the 
rolling circle, 2E, in determining the epi- and hypocy- 
cloidal curves is not a fixed diameter; however, it is 




Fig. 45 



MECHANICAL DRAWING 



45 



best to make it one-half the diameter of the pitch circle 
of the smaller of two engaging gears. In a problem 
where the diameter of PC, or 2R, and the number of 
teeth n are given, the circular pitch, which is the dis- 




46 



A PRACTICAL COURSE IN 



tance from one tooth to a corresponding point of an- 
other, CP, must be laid off first on PC. The involute 
method is as follows : At the radial line 2 draw a 
tangent 8 where it intersects the base circle at 2. 
Lay off on this tangent the chord of the arc of the PC 
between radials i and 2. This is a point of the curve 




Fiif. 46a 

of the tooth. Again at radial 3 repeat the above 
process, but lay off two chords of the arc on tangent 
9 instead of one; on 10 three chords, and so on 
until enough points are secured to define the desired 
involute tooth curve. Reverse the operations for the 

CP 
other side. — = the width of the tooth or space 

2 
for all purposes in drafting. The lower half of the 
profile of the tooth is a radial line. The base circle 



MECHANICAL DRAWING 47 

is drawn tangent to the involute line of 15'', through M. 
Practically the same principle is involved in laying 
out the cycloidal tooth except that the chords of arcl 
on PC are laid off on the arcs of the rolling circle 
Above the line PC the rolling circle generates the epi- 
cycloidal profile, or addendum, while below, the hypo- 
cycloidal or dedendum, A = E. 

The following additional data are given for those 
who would like to specialize on gear teeth and is ar- 
ranged from Kent, a well known authority : 
Addendum = depth of tooth above PC = .35 CP. ) p 
Dedendum = depth of tooth below PC = .35 CP. J ^ 
Clearance at root of space = .05 to .1 of CP. (C.) 
Actual thickness of tooth on PC = .45 of CP. \ 
Actual width of space on PC = .55 of CP. f * 

Backlash, or play between engaging teeth = .1 of 

v_^ J. . 

Circular pitch = a tooth and space on PC and is 
more commonly used than diametral pitch. 

Diametral pitch = a certain number of teeth per 
inch of diameter of PC. 

If DP = I CP = 3.1416. 
== 114 = 2.094. 
= 2 = 1.571. 

= 2}i = 1.396. 

= 2y2 = 1.257. 

From the above it is seen that a tt (pi) relation exists 
between circular and diametral pitch, i. e., if w be di- 
vided by DP the result will be CP; or if tt be divided 
by CP the result will be DP. 



Are about equal in machine cut gears. 



48 MECHANICAL DRAWING 

Let n = number of teeth. 

ttD 

CP = when D = diameter of PC. 

n 



IT. 



D 



CP 

The thickness of rim D := .12 + .4 CP. 
The width of face, W, Fig. 46a, averages 2 to 2^ 
CP. 

The diameter of hub = twice the diameter of shaft. 

Thickness of web connecting hub and rim varies. 

Arms are used on larger gears. Holes are often 
drilled through the web to lighten the weight without 
destroying the efficiency of the gear wheel. The length 
of the hub may be flush with the rim, but is usually 
Yx inch or more longer. 

The "face" of a tooth is the distance B above 
PC. The "flank" of a tooth is the distance B be- 
low PC. ''K," Fig. 46a, shows the position of the 
core print used in molding the hole for the shaft. 

Problem i. — Draw the front and side views of a 
gear wheel having 24 teeth, 2^ diametral pitch, with 
epicycloidal profile of teeth. Scale, full size. 

Problem 2. — A pinion for a certain gear has 2y 
teeth. CP is 1.571 inch. Draw forms of teeth by in- 
volute method. Scale, half size. 

Note : A pinion is the smaller of two gears acting 
together and should not have less than 12 teeth. 

Problem j. — A recent examination for a city high- 
school position contained the following question : 

Make a scale shop drawing of a pair of meshing 



50 A PRACTICAL COURSE IN 

gears of 8 diametral pitch. One gear to be a plain 
gear, to have ^2 teeth, i-inch face, i-inch bore, 
one hub ys inch long and to be the driver. The follow- 
ing gear to be a web gear and to travel at two-thirds 
as many r. p. m. (revolutions per minute) as the driver. 
The follower to have a 5/16-inch web, j4-inch rim or 
backing and 2-inch hubs, one hub being flush and the 
other J^-inch long. Each gear to be held on the shaft 
by two kinds of fastenings. All dimensions and de- 
tails, not here specified, to be assumed at the option of 
the draftsman to make the mechanism of ordinary 
and reasonable proportions. Driver and follower to 
be designated. Driver to be finished all over (f. a. o.) ; 
follower to be finished (f.) at rim, also on ends and 
outside of hubs. 

Note : Profile of teeth not necessary for cut gears. 
Scale, full or double size. 

Exercise 46. — Archimedean spiral of one whorl. 
Construction : With a radius equal to the rise of the 
spiral AB, and A as a center, describe a circle. Di- 
vide AB into as many equal divisions as the circle has 
been divided into sectors. Lay off successive arcs 
on the radials and draw in the curve. If a spiral of 
2 whorls is desired divide AB into twice as many parts 
as for one whorl. This problem represents a cross 
section of the Nautilus, a sea shell described by Oliver 
Wendell Holmes in 'The Chambered Nautilus." 
Fig. 47. 

Exercise 47. — Heart plate cam. Fig. 48. The con- 
struction for this common object may be derived from 
Exercise 46 and the figure. The sewing-machine bob- 
bin-winder is one of several applications of its use. 

Exercise 48, — The involute spiral. This curve is 
developed by unwinding a string wrapped about a 



MECHANICAL DRAWING 51 

cylinder, the end describing the involute. Construc- 
tion : Lay ofif tangents at regular intervals to the 
cylinder. On the first tangent line step ofif the chord 
of one arc. On the second tangent, two chords; on 




Fig:. 49 

the third, three, etc. Draw the curve through the 
points. Fig. 49. 

The involute is used in defining the tooth curve of a 
gear wheel. 

Exercise ^9— Helix. Fig. 50. A definition of a 
helix may be given as the combined vertical and hori- 



MECHANICAL DRAWING 



53 



zontal motion of a point about a right line as an axis, 
no two points of the curve lying in the same plane. 
The upper part of Fig. 50 shows this part laid out apart 
from its application to the screw thread. Construction : 
Lay out the plan and elevation of the thread desired. 




Fig. 51 



54 



A PRACTICAL COURSE IN 




Fig. 52 



Fig. 53 



MECHANICAL DRAWING 



55 



Divide the half section of the plan into any number 
of equal parts and divide the pitch into as many. The 
curves are obvious from the illustration, which is a 
single thread. By a single thread is meant the wind- 
ing of one screw thread about the bolt-cylinder. A 
double requires two threads parallel to each other; a 
triple, three, and a quadruple, four. Fig. 55 represents 
a conventional method of showing the single thread 
in practice. No attention is paid to the theoretical 
helical curve in drafting; however, it is essential to 
have a proper understanding of it. 




Fig. 54 



Exercise 30. — Ionic volute. Figs. 51, 52, 53 and 54. 
Fig. 51 is an illustration of the volute spiral of an Ionic 
capital in classic architecture (Fig. 54). In laying 



56 



A PRACTICAL COURSE IN 



out such a curve, either method. Fig. 52 or Fig. 53, 
may be used with the same results. When AB is given 
(Fig. 51), make the eye of the volute 1/16 of AB and 
locate its center on the ninth division of AB. Divide 




Fig. 55 

the semi-diagonal of the square into three equal parts 
and construct squares through these points, as in Fig. 
52. Each corner of these squares is a center for quad- 
rants of the outer spiral starting with radius A. The 
inner dotted squares are drawn to pair within the 
first squares, a distance of one-third the space between 
the first series of squares. Proceed with the construc- 
tion of the spiral following consecutive radii. 

The second method is practically the same as the 
first, just described. The radii of the first quadrants, 
both inner and outer, are taken on the line CD. Follow 
the unbroken lines until the spiral is completed. The 
construction of the diagonal in beginning this method 
is the same as in Fig. 52. The offset diagonal is equal 
to one of the smaller spaces on the diagonal. 

Exercise 5/. — Draw a i-inch bolt of 3 inches length. 
There are 8 threads per inch. The angle of the V's 
in the U. S. Standard or Sellers thread is 60°. Note 
the difference between a single and double V thread in 



MECHANICAL DRAWING 57 

the conventional layout. A square has half as many 
threads as a V of the same diameter. Show length of 
bolt from underneath edge of head to the end of the 
cylinder. Figs. 55 and 88. 

Ornamental and decorative art implies the use of 
geometry in laying out designs and patterns in stained 
or art glass, carpets, wall-paper, oil-cloth, borders, 
ornamental iron, woodwork and carving, carpentry and 
cabinetmaking, pottery, china painting, floor-tiling, and 
in bookbinding. Meyer, in his "Handbook of Orna- 
ment," says: "In medieval times these geometric con- 
structions developed into practical artistic forms as 
we now see them in Moorish paneled ceilings and 
Gothic tracery." In the exhibit of Indian relics in the 
Field Museum one may also see traces of geometric 
design in the tattoo and decoration of the imple- 
ments of the savage. The history of some of these de- 
signs is very interesting, particularly the Swastika and 
the Maltese cross. 

Geometric motives may be obtained from the flowers. 
The trilium, daisy, columbine and lilac are illustrations 
of the triangle, circle and polygon. These may be ar- 
ranged into rosettes, borders and stencils, using a cir- 
cle as a unit. 

The illustration of the trefoil. Fig. 32, is a design 
of a monogram of an appropriate initial. 

Problems pertaining to decorative design will not 
be given in this course, but will be reserved for a later 
work. 



CHAPTER IV 

WORKING DRAWINGS 



T^ LSEWHERE reference has been made to the 
^-^ value and importance of a working drawing in 
the shops. No rehable workman should attempt a new 
problem without a working drawing having previously 



/ 

• 
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/ 

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/ 








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"^ X 






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--^k/ 


T-</'~V'~' 


/ 


1 \ 


1 ^ 

1 / 

v 


II / 
V 






""A \ 1 


i \ 




i 1 

1 • 


1 




V 




1 i 

1 


\ p 
1 

1 
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1 

1 

1 


1 
i 


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Fig. 56 



been made. No first-class foreman should permit any 
other kind of a workman to begin a responsible task 
without having ample directions in plan and elevation. 
By a ''plan" is meant the appearance of the top of 
an object when observed from above. By ''elevation" 



58 



MECHANICAL DRAWING 



59 




Fig. 57 




Fig. 58 



60 A PRACTICAL COURSE IN 

is meant the appearance of the object when observed 
from the front or side. Having three views of the 
object, any ordinary problem in the shops may be made 
clear. Occasionally a very irregular object requires 
special views, but for our immediate purpose these will 
be omitted. 

Suppose a model be placed within a glass case and 
a plan view traced on the upper surface. Likewise 
trace a view of the front and side. Now open each 
plane until top, front and side lie in one flat surface 
as in Fig. 56. This is the working drawing, or three 
projected views. Both H and P planes revolve through 
90"^. Note the references to height (H), width (W), 
and depth (D), together with the method of obtaining 
them from one view and carrying to another, in Fig. 

57. 

If a glass case with hinged sides is not conveniently 
acquired select and invert a good pasteboard shoe-box 
over any geometric model. Sever all but the front 
edges, which are to serve as hinges. Outline on the 
surfaces the shape of the several views and then cut 
out the outline from the H, V and P planes. A chalk- 
box, pencil-box, prism, or any object which is simple 
in shape, will serve well as a drawing exercise. Many 
problems should be drawn to firmly fix the funda- 
mental principles of projection which underly the 
working drawing. While the geometric exercises form 
the basis of all mechanical drawing, the details and 
principles of the workman's drawing are the most 
used and practical application of constructive drawing. 

The craftsman, patternmaker, machinist or carpen- 
ter must each have a definite plan or idea prescribed 
before him in the form of a blueprint working drawing. 
The first thought of any constructive character must 



62 ' A PRACTICAL COURSE IN 

always first appear on paper, and the common means 
of that representation is the above-described kind of 
drawing. Fig. 58. 

PROBLEMS 

1. Draw three views of the rectangular prism. Fig. 

59- 

2. Draw three views of the pentagonal plinth. Fig. 

60. 

3. Draw two views of the bushing pattern. Fig. 61. 

4. Fig. 62 is a representation of an angle iron. 
Draw three views and dimensions. 

5. Fig. 63 is a drawing of a cast-iron block. Two 
views and dimensions. 

6. Fig. 64, pillow-block bearing. Three views and 
dimensions. 

7. Fig. 65, tool post holder. Three views and di- 
mensions. Scale half size. 

8. Fig. 66, rocker. Three views and dimensions. 

9. Fig. 67, crank arm. Two views and dimensions. 

10. Fig. 68, core box for pipe tee. Three views and 
dimensions. 

11. Fig. 69, coupling. Two views- and dimensions. 

12. Fig. 70, V block. Three views and dimensions. 

13. Fig. 71, drawing of a pattern for a shaft bear- 
ing without the cap. Draw three views. 



MECHANICAL DRAWING 




CHAPTER V 

CONVENTIONS USED IN DRAFTING ' 

/CONVENTIONS, as explained in a previous chap- 
^^ ter are customary methods or symbols established 
by usage and precedent and are generally employed for 
the sake of uniformity and convenience the world over. 
Their use and convenience will be readily understood 
by the student. 

a. Circles require two center lines, and must al- 
ways be shown. 

b. Invisible edges are shown by a series of ^-inch 
dashes with i/i6-inch space. 

c. Visible edge lines take precedence over invisible 
lines when they coincide. 

d. Dimension lines are very light, continuous, and 
broken only for dimensions, near the center. 

e. Dimensions should read at right angles to the 
dimension lines in the working drawing. 

/. Sharp, snappy arrow-heads should attach to the 
ends of each dimension line. 

g. The summation, or aggregate of several dimen- 
sions tending in any one direction, should be shown 
separately, that the workman may not err in calculat- 
ing the over-all sizes of stock required for the finished 
product. 

h. Projection lines are light single dashes of 
any desirable length extending from view to view 
to facilitate the placing of the dimensions. They should 
not touch the projections of the figure. 

i. Space too small for dimensions should have ar- 

70 



MECHANICAL DRAWING 71 

rows outside and directing toward the space to be 
dimensioned. 

;. The draftsman's figures are to be used for all 
numerals, or fractions, which must be common shop 
units, as 3V, t'V^ h f- etc., and not -|, |, 
To? tV- The bar which separates the numerator 
from the denominator should always be horizontal to 
avoid any possible mistake in reading a dimension. 

k. Section planes have the same convention as cen- 
ter lines. 

/. All edges of material which are shown cut by 
a plane in the drawing, are solid lines. 

m. Adjacent pieces in an assembly of parts must 
be crosshatched at right angles, or in dififerent direc- 
tions. Do not space too closely. 

71. Dimensions are not so likely to be overlooked 
by the w^orkman if placed to the right and between 
the views as much as possible. 

G. Do not permit dimension lines to cross each 
other. 

p. Show dimensions between center lines and ''fin- 
ished" surfaces. They are most important in any 
drawing. 

q. Sections are shown to make clear hidden details 
of construction. They should be frequent and prop- 
erly located in complex drawings. 

r. Do not repeat dimensions except in a very com- 
plicated drawing. 

s. Always place full-size dimensions on the draw- 
ing, no matter what scale is used. 
t. Locate the ''front" elevation first. 
li. Invisible parts behind sections are never shown. 



72 A PRACTICAL COURSE IN 

V, Bolts, shafts and screws are never sectioned. 
A broken cross-section of a bolt or shaft should show 
the convention of material. 

w. Show diameters in preference to radii. 

X, Never cross-hatch over dimensions. 

y. Arcs of circles and curves should be drawn be- 
fore straight lines which adjoin them. 

LETTERING 

One of the most important features of any draw- 
ing, and one most neglected on the part of a- student 
or amateur draftsman, is the neat appearance of every 
detail. These details consist chiefly of letters, figures, 
notes, titles, scales, stock lists and bills of materials 
— data which, if executed neatly and with precision, 
increase the appearance a hundred-fold of what might 
otherwise be a poor drawing. 

Architectural and mechanical draftsmen are obliged 
to letter well to retain their positions in many concerns 
although they may be expert in draftsmanship. Com- 
petitive and Patent Office drawings must, of necessity, 
lock neat in every particular in order to receive a con- 
sideration of merit. This is why technical schools 
insist, with emphasis, upon this additional good quality 
of their student's work. 

Notebooks, examination papers, programs and 
themes appear much better when their titles are well 
lettered than when scribbled in some unreadable char- 
acters. 

Note to the Teacher : A better impression of a student is 
derived from the manner in which he presents his work, than 
from how much work he presents. Insist that what he does 
be done well, and what he lacks in quantity will be more than 
made up in quality. 

If cross-sectioned paper is not available, it will be 



/ ■-. 



MECHANICAL DRAWING 73 

THE FOLLOWING IS A GOOD EXERCISE 
AND CONTAINS ALL THE LETTERS OF 
THE ALPHABET:- 

"THE quick brown FOX JUMPS OVER 
THE LAZY dog" 

HARD PRACTICE IS A GOOD MASTER. 
THE DRAFTSMAN'S FIGURES ARE AL- 
WA YS USED. 12 3^56 7 Q 9 O £ !§" 

ALL LETTERS AND FIGURES SLOPE 
HALF THEIR HEIGHT, OR ABOUT 30° 

Fig. 72 



7?}is lower case style is a very 
popular form of letters for notes, 
titles, stock-lists, bills of material, etc. 

"a quick brown fox jumps over 
the lazy dog" 

Stem letters are ,%ths of an inch 
high. Use a ballpointed pen **506 or 

A Bpb'ErGHiJkL M^ 



Fig. 73 



74 



A PRACTICAL COURSE IN 



well to ''rule'' a sheet into ^-inch squares and draw 
''slope" lines about 30° from a vertical, as in Fig. "j^. 
Pencil all letters freehand for guides, with a 2H 
pencil, and submit for approval. (Note: Do not mis- 
take a No. 2 pencil for a 2H. Any good stationer will 
explain the grading of pencils.) Ink with Iliggins' 
India ink and ball-pointed pen, No. 506, or 516. 

Fig. 'J2 is an exercise which contains all the letters 
of the alphabet. Some such sentence as this is usually 





■one 


TITLE 


t_ 

r 




iO|(g 


NAME OF SCHOOL 




SCALE, DATE, 


-^: 


PLATE NO., NAME 


=-100 


. 3i" . 





Fig. 74 

given in commercial schools to develop skill on the 
typewriter. Lower-case or small letters are shown in 
I'ig" 73- ''Lower-case" is a printers' term, printers' 
type cases being so arranged that the capital letters 
are contained in the upper and the small letters in the 
lower compartments. In Fig. 74, a title is shown. 
Note that the most important part of the title is the 
object of the drawing and hence should be more prom- 
inent than the rest. A title should be so balanced that 
one side will not appear to "see-saw" or be heavier 
tlian the other. All drawings should be titled prop- 



MECHANICAL DRAWING 75 



TH/S FREEHAND GOTHIC STYLE OF 
LETTERS SHOULD BE USED ON ALL 
DRAWINGS NOT ARCHITECTURAL OR 
TOPOGRAPHICAL. 

MAKE ALL LETTERS UNIFORMLY 
HIGH, ^TH INCH IF LOWER CASE 
AND JtH if caps. THIS STYLE IS 
^TH CAPS. 

DRAW LIGHT GUIDE LINES FOR 
THE SLOPE AND HEIGHT. WIDE LET- 
TERS ARE BEST SPACE BETWEEN 
WORDS SHOULD NOT BE LESS THAN 
J[TH INCH, NOR MORE THAN §THS. 
KEEP LETTERS IN EACH WORD COMPACT 

GOOD LETTERING ENHANCES THE 
APPEARANCE OF ANY DRAWING. 

NEATNESS AND LEGIBILITY ARE 
VALUABLE ASSETS IN MECHANICAL 
DRAWING. 

DO NOT USE A VERTICAL STYLE. 

Fie. 75 



76 MECHANICAL DRAWING 

erly. The titles need not be circumscribed by a 2x3^- 
inch boundary, but the proportion of the spacing be- 
tween lines and heights should remain as in the illus- 
tration. Place the title plate in the lower right-hand 
corner, about Yi inch from the margin line. 



aabcdefghvjklmnopqrs-t 
uvwxyz 

ajbcde^MjMmnopqrs'i: 



Figf. 76 

Oval letters and figures are constructed on the form 
of the letter ^^O.'^ Make the letter ^'O" and then 
modify to suit the shape of the desired letter or figure. 

Draw all downward strokes first, then curves or in- 
tervening fines as indicated in Fig. y^- 

Practice lettering the exercise given in Fig. 75 until 
proficiency is assured. 

Fig. 76 is an architectural style of letter. 



CHAPTER VI 

MODIFIED POSITIONS OF THE OBJECT 

C UPPOSE the prism in Fig. 59 (Page 61) be re- 
^ volved about a vertical axis, i. e., an axis 1 (per- 
pendicular) to the H plane. Looking down on the 
prism in Fig. 59, how would the plan be drawn if the 



A 


^«v^ 






V 


/ 


/ 


/ 






/ 


L 


G 




/ 






/ 








/ 




























\ 
\ 
\ 
\ 

1 
i 

\ 
\ 

L 





L 
Fig, 11 

object be revolved 30° about a vertical axis? Does 
the altitude and the construction of the plan view alter 
in such a revolution? Use the chalk-box as a model 
until each step in the thinking process is clear. Now 
draw the remaining views. Through how many de- 

77 



78 



A PRACTICAL COURSE IN 



grees does the earth revolve? May anything revolve? 
Any point of the object always moves in a plane 1 
to the axis. There are 360 degrees in a circle. 

Principle i. — When an object revolves about a ver- 
tical axis (1 to H) its plan view is not altered in shape, 



/ 


/ 


/ 


X 




\ 


\ 


V 


/ 


6 








/ 

/ 
/ 
/ 
/ 
/ 
/ 
/ 
/ 

/ 
/ 

/ 
/ 




/ 




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L 
















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) 


7 












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K. 


/ 
/ 












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y^ 


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/ 




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X 




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/ 
/ 


/ 












/ 


/ 




y 




\J 


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L ' 


X 



Fig. 78 

but only in position, and the height remains the same. 
Fig. yy. 

Note : No distinction is here made between 'Ver- 
tical" and ''perpendicular," as the H plane is always 
considered horizontal. 



MECHANICAL DRAWING 79 

Find the projections of the pHnth in Fig. 60 (p. 61) 
when it is revolved through an angle of 30° about a 
side axis, i. e., // (parallel) to the profile or side plane. 

The observer will note here that each point of the 
object revolves in a circular plane, or path, through 
30°, about the side axis, which can only be seen as 
a point from the front. Therefore, the front elevation 
will not be altered in construction from its original and 
natural position, but its position will be 30° inclined 
to the base upon which it originally lay. Find its re- 
maining projections. Looking down on the plinth in 
Fig. 60, as on the prism, when it is revolved about a 
side axis (1 to V) we discover that the depth or thick- 
ness does not alter, but the construction of the plan 
changes. 

Principle 2. — When the object revolves about a side 
axis (1 to V) to the right or left, its front elevation 
does not change, save its position, and the depth (D) 
remains the same. Fig. 78. 

Find the three views of the frustum of the pyramid, 
Fig. 79, when it is revolved through an angle of 30°, 
forward or backward, about a front axis (1 to P). 

In this instance we must first observe the position of 
the object from the profile or right-side plane. The 
revolution about the front axis, which may be seen 
as a line parallel to the ground line, GL, and pass- 
ing through the center of the model, is then accom- 
plished by tilting the side elevation forward or back- 
ward, the lower edge making the required angle with 
the base upon which the object stands. Looking down 
on the prism in Fig. 59, again, it will be seen that the 
width of the object does not alter when it is revolved 
forw^ard or backward. Draw the three projections 
when so revolved, commencing with the side, then the 



80 



MECHANICAL DRAWING 



front, and the plan last. In this case all points of 
the object revolve in planes, which the observer can 
only see as straight lines // to VL. 




Fig. 79 



Principle 3. — When the object revolves about a front 
axis (1 to P), forward or backward, its side elevation 
does not change save in its position, and the width re- 
mains the same. 



CHAPTER VII 

THE DETAILED WORKING DRAWING 

\ MACHINE is a composition of many parts. 
-^^ Each part performs a certain function and bears 
a close relation to adjacent members. If a mechanic 
desires to make a machine, he must organize the parts 
perfectly so that a minimum amount of friction is had 
to do the required work. When each part is made in 
the shops every specific detail is worked out separately. 
In the problem of the connecting rod, every detail is 
illustrated in such a manner that it will be very easy 
to imagine the size, shape, and to some degree, at least, 
the relative position of the parts when assembled to- 
gether. The connecting rod carries the power direct 
from the cylinder through the piston to the drivers of 
a locomotive. This object is a detail of a stationary 
engine. A detailed working drawing is made to enable 
the mechanic to construct each detail without con- 
fusion. 

From the illustrations make a working drawing of 
each separate part, and then fit them together in an 
assembly drawing. 

Figs. 80 and 81 are parts of a bearing which sur- 
round the cross-head pin and fit in the left-hand end 
of the rod. Fig. 87. Fig. 82 is a tapered key-block used 
to take up wear and is located behind Fig. 80. Figs. 83 
and 84 are parts of the bearing which fit around the 
crank-pin and are located on the right end of the 
rod. Fig. 87. A strap. Fig. 85, holds these two parts 
together with another tapered key-block. Fig. 86, by 
means of half-inch bolts. Two ^-in. bolts, 6 in. long. 
Fig. 88, fasten the strap to the rod. Each tapered key- 
si 



84 



A PRACTICAL COURSE IN 



'^. 







-^o£- 



^ ^ "H 






tV-\^-V4A 



\ 




Fig. 85 




Fie. 86 



MECHANICAL DRAWING 



85 



block has iwo ^-inch bolts, one on each side of the 
strap. This makes six bolts in all. The hole on the 
end of the strap is for oil. Copy in Gothic slant letters 
the stock list. Fig. 89. 







Fig. 87 



When the drawing of a machine problem is com- 
pleted, it is first sent to the patternmaker, who makes 
a model in wood from it. He must know from ex- 
perience the amount of material to allow for shrinkage 



gPiN Key 




Fig. 88 



of the casting in cooling, how much to allow for polish- 
ing or ''finishing," and how much taper for ''draft'' in 
withdrawing the pattern from the mold. The pattern 
is then sent to the foundry, where it is molded in sand. 
After the form has been made it is "poured,'' that is. 



86 A PRACTICAL COURSE IN 

tilled with melted ore from the cupola. When the cast- 
ing is cool enough to handle, it is sent to the machine- 
shop to be machined and ''dressed'' ready for use. 
Here, again, the working drawing must be brought 

5 TOOK LIST 




MARK 


A/a 

WANT 


NAME 


MATERIAL 


REMARKS 




80-ai 


/ 


BEARING 


PH. BRONZE 


2 PARTS 


82 


/ 


KEY-BLOCK 


STEEL 


EA.O. 


86 


/ 


II II 


It 


II 


83-84 


1 


BEARING 


PH.BRONZE 


FINISH 
BABBI TT 


85 


/ 


STRAP 


STEEL 


F.A.O. 


87 


/ 


ROD 


tt 


II 


88 


a 


BOLTS 


W.I. 


6"x/0 




1 


It 


It 


3 "Xfo 




2 


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II 


'i'xfo 




1 


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1 II in 

1^ X^D 


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t 
r 

a 


Fig. 89 

nto use, for the machinist is obliged to follow th 
pecifications thereon, regardless of what he migh 
hink ought to be done in the case. This places all th 
esponsibility of error upon the draftsman. 

A detailed working drawing, as applied to the wooc 
vorking and building trades, is also a very importar 
ipplication of the working drawing. It is fully a 


e 
It 
e 

1- 

Lt 

S 



MECHANICAL DRAWING 



87 




e^6J0/5TS 



Figf. 90 



necessary that such a drawing be as carefully made for 
the carpenter or cabinetmaker as for the machinist or 
engmeer, and no skilled workman should attempt a 
task requiring skill and accuracy without it. 



88 



A PRACTICAL COURSE IN 



For erecting the framework of a cottage, details 
specific and clear must accompany the plans and eleva- 
tions. vStuds, sills, rafters, sashes, joists, etc., should 






Fig. 91 



be so located as to give the greatest service. Fig. 90 
shows an isometric representation of a framing detail, 
and, although not in accordance with the orthographic 
working drawing, shows to an untrained imagination 



MECHANICAL DRAWING 



89 



a better idea of the construction. Note the dimensions 
between members, size of stock and joinery. The 
plate, at A, for the second floor, is usually set in an 
inch in the studding. This is called a gained joint. 




NESNEL 
P03T6'^6 



Fi&.92 



Other forms of joints are miter, tongue-and-groove, 
tenon-and-mortise {C), dovetail (K) , half -end lap (D), 
bridge (B), butt (F) and open tenon with key, each 
having a special purpose for its use. Fig. 91. 

Problem i. — Make an assembled drawing — plan and 



90 MECHANICAL DRAWING 

front elevation— of the framing details suggested in 
Fig. 90, and dimension properly. Scale i>^ inch == i 
foot. 

Problem 2. — As in Problem i, make a drawing of 
the stair detail. Risers, 7" ; tread, 10'' wide. Balus- 
ters 2" square and space equal to the width of baluster. 
Fig. 92. 

Problem 3, — Make a working drawing of the forms 
of joints used in joining represented in the illustration. 
Scale, half-size. Dimension. Use stock sizes of ma- 
terials. Fig. 91. 

Problem 4. — Make a floor plan of your home, 
a barn or school-room, and show all appointments. 
Scale Ys" to the foot. Small details are usually drawn 
larger or to full scale. 

Problem 5. — An examination in high-school draw- 
ing included the following: Make to scale >4" to i' 
arT architect's plan for the upper five-room flat in a 
modern three-story building. Show by the customary 
architectural conventions all that is necessary and 
usual. Outside dimension 22' 6^x36^ 



CHAPTER VIII 

PATTERN-WORKSHOP DRAWINGS 

/^ NE of the most useful applications of the working 
^^ drawing is the laying out of patterns, or devel- 
opments. The theory of such a drawing is found in 
the study of Descriptive Geometry — a science which 
all architects and engineers are required to know some- 
thing about and which is extremely useful to drafts- 
men, although often avoided. 

A thorough knowledge of the principles of pattern- 
making enables the tinsmith or sheet-metal worker to 
lay out very complicated patterns in a very simple geo- 
metric manner and thereby save time and material to 
all concerned. Cutting a pattern so as to be as econ- 
omical as possible, requires foresight which the usual 
patternmaker fails to exercise. Tin-plate scraps often 
may be used to as good or better advantage than new 
sheets, if conservatively and thoughtfully cut, and in 
all kinds of work stock should be ordered so that a 
minimum amount of waste is left. 

A pattern is a plane surface representing the un- 
folded sides of an object equal to the perimeter of its 
right section, the width equal to the altitude of the 
object, or, rather, the true length of its lateral surface. 

Develop the surface of a cylinder or prism upon a 
sheet of bristol paper, allowing ^ inch for lap. Glue 
the lap and fasten together for a facsimile of the orig- 
inal. Add bottom and top. 

In most cases, in beginning a problem, it is only nec- 
essary to draw the plan and front elevation plus an 
auxiliary sectional view to show the true size of the cut 
section. From any of the illustrations, Figs. 93 and 

91 



MECHANICAL DRAWING 



93 



95, it will be seen that the object is projected up into 
the plane of the paper to obtain the auxiliary view. 
After the pattern is draw^n it is transferred from the 




manila or bristol paper to the metal by pricking points 
with a sharp punch along the contour of the pattern, 
due allowance being made for lap and seam. The 
double edge shown on the development of the quart 
measure is for the lock seam shown at A, Fig. lOO. 



94 



A PRACTICAL COURSE IN 



PARALLEL METHOD 

Problem /.—A truncated hexagonal prism is to be 
developed as shown in Figs. 93 and 94. Use any suit- 
able dimensions. Construction: Draw the plan and 




Fig:. 96 

elevation, also sectional view, as at A. The width of 
the section and base is the same as the depth of the 
prism transferred from the plan view. In the "layout" 
the various heights of the linear elements of the prism 
are laid ofif on corresponding parallels in a straight line, 
equal in length to the perimeter of the base. ^ 

Problem 2,— A truncated hexagonal pyramid is to be 
developed, as shown in Figs. 95 and 96, to suitable 



MECHANICAL DRAWING 






Fig:. 97 



Fiif. 99 




Fig:. 98 



96 



A PRACTICAL COURSE IN 



dimensions. Construction: Obtain the projections 
and sectional view as in Problem i. To obtain the 
development it is necessary to know the slant height 
of the pyramid. The exterior edges are parallel to the 
vertical plane ; therefore, their true lengths must be 
seen at AC. With a compass set with AC as a radius. 




Fig. 100 

describe an arc. Lay off the perimeter of the base on 
this arc and join all points with radial lines to the 
center of the arc C. Step off the true length of each 
cut element, o, i, 2, 3, shown projected on AC; then 
join as in Fig. 96. To complete the pattern add the 
section and the base. 

Problem j. — Develop a frustum of a rectangular 
pyramid, base 2"xi34" and altitude 3''. 

Problem 4. — An irregular cone is projected in Fig. 
97. Develop by radial lines as in Fig. 96, except that 
the true length of each element be found separately. 



MECHANICAL DRAWING 97 

Problem 5. — Given the front elevation of a ij/^" 
cylinder, Fig. 98, draw the plan and develop. 

Problem 6. — Draw the pattern of a quart measure, 
Figs. 99 and 100, diameter of upper base 3'', lower 5''. 
Find the altitude. Note : This problem involves a 
principle of mensuration. Use either dry or liquid 
measure. 

V V 

= A, or = A, 

.R2 D2 (.7854) 

where V =: the volume, or solid contents and A = 
the altitude. This is approximate. To be exact, the 
formula should be stated as follows : 



\ a + ^ + yj a/^ ff = ^^ 



[3 

when a = area of upper base. 
b =: area of lower base. 
h = height or altitude. 

There are 231 cubic inches in a liquid gallon and 
2150.42 cubic inches in a bushel. 

The problem here indicated is one of finding the 
altitude of the frustum of a cone. vSubstitute the 
known value of V, the volume, and solve for h as in 
any equation. 

Fashion a suitable strip for a handle allowing ^" 
lap for edges. The illustration, E, Fig. 99, shows the 
lap over a wire at the top of the cup. A customary 
rule for lap is 4 X thickness of metal -{- twice the 
diameter of wire. 

Problem 7. — An irregular triangular pyramid having 
an altitude of 4^", the sides of its base 2" or more 
in length and all lateral edges oblique to all planes 
of projection, has two lateral edges and base cut by a 



98 A PRACTICAL COURSE IN 

sectional plane perpendicular to V and oblique to H. 
Draw the three orthographic views and the true size 
of the section. Develop. Figs. loi and 102. 

Problem 8. — An irregular oblique quadrilateral 
prism has a right section resembling Fig. 103. Use 
suitable dimensions. Its axis is inclined 30° to the 
right of its base, which is horrzontal. A plane inclined 
60° to the left of its base cuts all the lateral edges of 
the pdsm. Draw the three projections and the auxil- 
iary or sectional view. Develop, adding the base and 
sectional view. 

Problem 9. — Draw three views of a regular vertical 
pentagonal pyramid, with apex above the base. The 
rear edge of the base is inclined 15° to the vertical 
plane of projection, V, the left end of this edge to be 
nearest V. The diameter of the circumscribing circle 
of the base is 2" and altitude 4". The pyramid is cut 
by a plane perpendicular to V and at an angle of 60° 
to its base. Show the line of intersection in three 
views, make a sectional view, and develop either trun- 
cated part. 

Problem 10. — A circular ventilator projects, through 
a gambrel roof as shown in Fig. 104. Work out the 
line of its penetration wnth the roof planes. Develop 
the ventilator top and also the roof planes, showing 
the line of penetration. Scale i" = 1^0". 

Problem 11. — Develop a truncated right cone from 
the illustration. Fig. 105. 

Note: Problems 7, 8, 9 and 10 are intended as 
test problems. 

Any development of a geometric form is a mathe- 
matical process, and hence should receive some such 
consideration. 



MECHANICAL DRAWING 



99 




Fig. 101 




Fig:- 102 



100 A PRACTICAL COURSE IN 

The following formulas are self-evident and should 
be committed to memory : 

27rR = the circumference of a circle. 

7rR2 ziz area of a circle. 

(7rR2)L = volume of a cylinder when L altitudcc 

(27rR)L = lateral surface of cylinder. 

(7rR^)L/3 = volume of cone. 

(27rR)S/2= lateral surface of a cone when S = 
slant height. 

6(XY/2) = area of a hexagon when X == one side 
of the polygon and Y = the apothem. 

Note : The apothem of a polygon is the perpendicu- 
lar distance from the center of a polygon to one of its 
sides. 

6(XY/2)L = volume of a hexagonal prism. 

6(XL) = lateral surface of a hexagonal prism. 

(2^R)D = lateral surface of a sphere when D — 
diameter. 

Problem 12. — Develop a cylinder when R = ^", 
L = 3"- 

Problem jj. — Develop a cone when R is given and 
the volume. 

Problem 14. — The area of an octagon is 24 square 
inches. X = ^". Develop full size. 

Problem 75.— Y = ^'', L = 2>4". Develop. 

Note : This problem involves a geometric construc- 
tion of a hexagon without a circle before a develop- 
ment can be made. Using different data, originate 
and solve other problems. 

Problem 16. — Fig. 106 shows the form of a sheet- 
metal hood for a forge. Scale, half size. 



MECHANICAL DRAWING 



101 




Fig. 105 



102 




Fig. 107 





J \ 




/ '. 


103 








n 






/ 




t 




/ 


\ 




/ 


\ 


/ 


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/ 


I 


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1 


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\ 1 


o 










o> 




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® 


L 






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\ 


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\ 




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\ 




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\ 


V 






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-V. 






1 


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V r 





104 



A PRACTICAL COURSE IN 



Problem //.—Fig. 107 gives the front elevation of 
of 6" stove pipe elbow, and Fig. 108 the development 
of a large and small section. 

Problem 7^.— Develop a 3" sphere by the "orange 
peel" method. Fig. 109. 




Fig. 109 

Problem 79— Secure a good model of a funnel and 
draw out the pattern. 

METHOD OF TRIANGLES 

Problem 20.— Tapering ventilator collar. Many 
problems are impossible to develop by either method 
previouslv referred to. on account of their surfaces 
being warped. A warped surface cannot be laid out 



MECHANICAL DRAWING 



105 



geometrically, but it can be constructed approximately 
by means of triangles. The mold-board of a plow, 
''cowcatcher" of a locomotive, marine ventilator fun- 
nels, grain elevator spouts, a cow's horn, stacks, coal 




Fie. 110 



106 A PRACTICAL COURSE IN 

scuttles, footballs, and similar objects with irregular 
surfaces, are non-developable except by the approxi- 
mate method above referred to. Construction: Lay 
off on the projections of the figure small triangles at 
regular intervals, determine their true size and lay ad- 



Fig:. Ill 
jacent to each other. This will constitute, as near as 
may be done, a working pattern. The base of each 
triangle is shown in the plan view, the altitude in the 
elevation. Fig. no. 

The hypotenuse of any right-angle triangle is easily 
determined when two of its sides are known. Devel- 
opment (Fig. in) : Lay off at any convenient place 
a radial, and for our purpose we will select the long- 
est. At the lower end strike an arc equal to X-2 on 
the sectional view of the roof plane. With center at 
2', Fig. Ill, and radius equal to the length of the first 
diagonal 1-2", intersect the small arc 1-2". Small 
arcs are equal to C-D. With center 2" and radius 
1-3 strike arc at X, then lay off second radial on 
either side of first radial, 1-2'. Repeat until all radials 
and diagonals have been used. Any w^arp surface 
may be developed in this manner. 



MECHANICAL DRAWING 



107 




Fig. 112 



108 



A PRACTICAL COURSE IN 



Problem 21. — Select a kitchen utensil which pri- 
marily must be laid out in pattern and make a develop- 
ment to scale. A dust-pan, roasting-pan, coffee-urn, 
colander or coal scuttle is suggested. Use any method 




Fig. 113 

or combination of methods, but be sure to determine 
whether the surface can be developed, or is warped, 
or any part thereof. Develop a truncated, irregular 
cone, Fig. 97 (page 95), by triangles. 

DEVELOPMENT BY REVOLUTION 

Fig. 112. This method is not so practical, but is 
more mathematically exact than former methods re- 
ferred to and is especially used to verify the radial 



MECHANICAL DRAWING 109 

line method. In geometry we are told that a point 
revolves about an axis in a plane perpendicular to 
the axis. This holds true here, for the upper edges of 
the truncated section revolve in perpendicular paths to 
the lower edge of the base. The length of the radius 
of revolution is determined by constructing a right- 
angle triangle one side of which always equals the dis- 
tance AX from the horizontal projection of the point 
A to the axis 1-2 in the plan, — the other of the per- 
pendicular altitude, A'-D^, from the vertical pro- 
jection to the plane of the base. The hypotenuse must 
equal RX. Connect i-R, which is the true length of 
i-A. This interesting exercise should be repeated 
until every step is clear. It is a graphical explanation 
of the same process in mensuration. 

A second method, and closely related to the above, 
is to find the true length of each edge of the truncated 
pyramid and lay oflf these true lengths on the paths of 
revolution as drawn through the upper points A, E, F, 
G, etc., from points of the base X, to R. The method 
of finding the true length of I'-A" is shown by re- 
volving i-A parallel to GL and projecting to the 
base of the pyramid I^ then moving to its revolved 
position and A' also. The true length of I'-A' is now 
shown at i"-A". Fig. 113 is an isometric illustra- 
tion of the above. 



CHAPTER IX 

PENETRATIONS 

V\7'HEN one object intersects or penetrates an- 
^ ^ other, the line of intersection of the two is 
defined where they meet. To determine the pattern 
this line must always be geometrically located, as in 
Fig. 114, and herein lies, very frequently, a difficult 
problem if the subject of working drawings and pro- 
jections has not been thoroughly mastered. 




MECHANICAL DRAWING 



111 



DEVELOPMENT BY PARALLEL PLANES 

Problem i, — Fig. 114 is an illustration of two inter- 
secting pipes. First, draw the plan and front eleva- 
tion. Conceive a series of parallel planes, A, B, C, D, 
E, F, G, cutting through both pipes and parallel to 




Fig. 115 

the front elevation. Each plane cuts two elements 
from each pipe, and all of the four elements lie in 
the same plane. In this case, two elements of pipe B 
penetrate one element of pipe A. Determine the pro- 
jections of each element thus cut, and where they 
intersect is a point of penetration. 

To develop either A or B, lay out the perimeter of 
a right section, the height of the pattern being equiva- 



112 A PRACTICAL COURSE IN 

lent to the length of the elements from the end of the 
cylinder to the line of penetration. 

A right sectional view 3hows the shortest possible 
circumference or perimeter of the object and is deter- 
mined by a plane perpendicular to the axis of the 
figure. 

Problem 2. — Fig. 115 represents a small rhombic 
prism penetrating a larger one, the top of each being 
a square in plan. Establish the lines of penetration in 
both plan and elevation, lay out the development of 
the smaller prism and develop the hole in the larger. 
Locate the line of penetration in the development of 
the smaller prism. A, B, C, D are planes passed 
parallel to the vertical plane. Find the projections of 
each element cut from both prisms. Where they meet, 
or intersect, determines the line of penetration, for 
each cut element lies in the same auxiliary plane. Num- 
ber each point, or letter with some familiar symbol. 
When objects are oblique to H or V pass a plane to 
determine the true perimeter of the right section. The 
trace of such a plane in this problem must be perpen- 
dicular to the lateral edges of either prism. The de- 
velopment must be made from this sectional line and 
in a similar manner to the layout of the hexagonal 
prism, Problem i, Fig. 94 (page 92). 

Problem j. — As in problems i and 2, find the line 
of penetration of a right cylinder with a right cone. 
Fig. 116. Pass horizontal planes. Axes of both fig- 
ures lie in the same plane. Use appropriate dimen- 
sions. Note that each plane cuts a circle from the 
cone and two elements from the cylinder. This is an 
illustration of a conical hopper connecting with a cyl- 
indrical pipe, or a gutter drip and rain-water pipe, as 
seen on many houses. 



MECHANICAL DRAWING 



113 



Problem 4, — A vertical pyramid 4" high, with a tri- 
angular base, length of one side 2^", one edge of base 
making 15° with V, is penetrated by a horizontal equi- 
lateral triangular prism, 4" long and perimeter of 63/''. 
One face is parallel to V and i" from the vertical axis 




Fig. 116 



114 



A PRACTICAL COURSE IN 



of the pyramid. The axis of the prism is 1^4" above 
the base. Draw three views full size, find the line of 
penetration and develop both objects. Figs. 117, 118 
and 119. 




Fig- 117 

Problem 5.— A conical steeple of a cylindrical tower 
is penetrated by the roof planes of a hip roof. Fig. 
120. Find the Hne of penetration and lay out the de- 
velopments of the conical roof and of the roof plane 
adjacent to the hip, showing the lines of penetration 
therein. Scale, ^" = 1^0". 

After drawing the plan and elevation from the illus- 
tration, Fig. 120, pass planes M, N, O and P to 
determine the line of penetration. As each plane is / 
to the base of the cone it will cut a true circle from the 
cone, as shown in the plan. It will also cut a line 



MECHANICAL DRAWING 



115 




from each roof plane parallel to the base of the hip 
roof. Where this element crosses the circle cut by the 
same plane is a point of penetration. A series of 
similarly acquired points will determine the line of 
intersection. 

To develop a roof plane revolve the point O of the 
upper corner of the hip into the same plane as the base 
of the cone and the roof, by the triangle metliod. O 




Fig:. 119 



116 



A PRACTICAL COURSE IN 







i 


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Fig. 120 



MECHANICAL DRAWING 



117 



moves in a plane 1 to the axis XY. Points lO, ii and 
12 move perpendicularly to the roof lines drawn 
through A, B and C. The development of the cone 
has been described. Fig. 121. 




Fig. 121 

Problem 6. — Develop the pattern for the base of a 
blower from dimensions given in Figs. 122 and 123. 
The right and left sides of this base are elliptical 
cylinders, that is, are not circular in cross section. The 
true size of the cross section cut by plane Tt' is show^n 
at X in the plan. This is the line of development, Tt', 
Fig. 123. The lengths of each element can easily be 
laid out and the triangular faces added. Draw to suit- 
able scale. 

Problem 7. — Develop the slope sheet of a locomotive 



118 



A PRACTICAL COURSE IN 




Fig. 122 

as given in Fig. 124, one-half to be developed by 
triangulation. This is one of several practical prob- 
lems to be derived from a study of the locomotive for 
purposes of developments. The steam-dome, sand- 
dome and smoke-stack are other illustrations of right 
cylinders penetrating the outside cover of the boiler 
and requiring templets or patterns. 




Fig. 123 



MECHANICAL DRAWING 



119 



Problem 8. — Draw the front elevation of the tran- 
sition piece and develop by triangles or the method sug- 
125. 



gested 



Fig. 




Fi^. 124 



Problem 9. — A regular vertical triangular prism, 
with a perimeter of 10^2" and 4'' altitude, has its front 
face inclined backward and to the left at is"". A right 



120 



MECHANICAL DRAWING 



square prism of 6^" perimeter and 4" altitude pene- 
trates the former. Axes of both soHds intersect at 
their center points. Develop both objects. 




Fig. 12s 



CHAPTER X 



ISOMETRIC WORKING DRAWING 

A N ISOMETRIC drawing is generally conceded to 
'^^ be a pictorial or perspective representation, and 
for practical purposes it has come to be eminently use- 
ful to the artisan in clarifying hidden constructions. 
Among draftsmen it has supplemented the freehand 
perspective sketch on account of the comparative ease 
with which the picture is made by the instruments. 

The few principles of isometric drawing may briefly 
be summed up as follows : 

a. All vertical edges in the object are vertical in the 
drawing, as in freehand. 

b. All horizontal edges, representing right angles 




122 



A PRACTICAL COURSE IN 



orthographically, make 30° to the horizontal in the 
isometric construction. 

c. Non-isometric lines of edges making other than 
right angles must be laid ofif orthographically first and 
then transferred to the isometric drawing. This dis- 
torts the true length of non-isometric Hnes, but does 
not mar the pictorial effect. 




Fig. 127 

d. Surfaces, not lying in the same plane, are estab- 
lished from center-isometric axes. 

e. Isometric circles are drawn within isometric 
squares of the same diameter as the given circle. 
Elliptic or irregular curves are constructed flat, then 
transferred. Fig. 126. 



MECHANICAL DRAWING 



123 




Fig. 128 



i24 A PRACTICAL COURSE IN 

/. Isometric workshop drawings are dimensioned- 
Dimensions must be placed parallel to the isometric 
lines. Fig. 127. 

g. The usual custom of shading an isometric draw- 
ing is to accent the edges separating light surfaces from 
dark, assuming the light to come from the left at an 
angle of 45°. A better method, and one which en- 
hances the pictorial effect, is to shade all edges which 
are nearest the observer's eye. This tends to lift the 
drawing of the object from the paper and relieve the 
unnatural effect of the isometric construction. Fig. 
127 is an illustration of the stub end of a connecting 
rod and exemplifies the second method described above. 
There are many draftsmen, however, who do not shade 
any drawings. The true purpose of shading is to 
make the drawing more attractive, but aside from this 
it has no value. 

h. Invisible lines are seldom shown in isometric 
drawings except where irregular lines are hidden by 
regular surfaces and the information desired can in no 
other way be shown. 

The illustrations in the text have largely been un- 
shaded isometric drawings of objects used in the class- 
room. 

Problem i. — Make an isometric drawing of a chalk 
or cigar box with the lid open. Scale, half size. No 
dimensions. 

Problem 2. — Select a good-sized spool. Draw in 
isometric. Scale, double size. No dimensions. 

Problem 3. — Copy the exercise of the connecting rod. 
Fig. 127. Scale, full size. Dimension. 

Problem 4. — Figure 128 represents the base and cap 



MECHANICAL DRAWING 



125 



of a pattern for a pillow-block bearing. Scale, full 
size. Dimension. 

Problem 5. — The teacher's desk to suitable scale. 
Do not show invisible lines. Dimension. Substitute 
a book-case. 

Problem 6. — A mission chair. Look for non-iso- 
metric lines. Dimension, and draw to suitable scale. 

Problem 7. — A shaft-hanger. Scale, half size. Iso- 
metric. Fig. 129. 




Fig. 129 



CHAPTER XI 

MISCELLANEOUS EXERCISES 

Problem /. — To construct the arc of a circle me- 
chanically when it is inconvenient to determine its 
radius, Fig. 130, make AB the chord of the arc ACB ; 
DC and ACB to be kept constant and the position 
changed so that points A and B remain in contact with 
lines AC and BC. The resultant points will determine 
the center and circumference of the required circle. 
The same problem might be constructed if strips be 
nailed together as the lines AC and BC suggest with 
a third strip crossing lines AC and BC parallel to AB, 
anywhere, to hold the angle firmly thus made. 

Problem 2. — A graphical method for finding the 
distance AB across a pond when the land in triangle 
FED is inaccessible. Set a stake at C in line with AB 
prolonged. Set another, D, so that C and B can be 
seen from it. Also a third stake, E, in line with BD 
prolonged so that DE equals BD. Set a fourth stake, 
F, at the intersection of EA and CD. Measure AC, 
AF and FE. Show that AB is a fourth proportional 
to AF, AC and (FE— AF). Draw a line through D 
parallel to AB. D bisects BE. DX is always AB. 
Fig. 131. 2- 

Problem 5. — Draw an involute cam which involves 
the construction of the involute curve on page 51. 

A cam is a very useful mechanical device which 
gives various motions to machine parts at regular in- 
tervals of time. It is generally in the form of a flat 

126 



MECHANICAL DRAWING 
C 



127 




Fig:. 130 




disk, although sometimes cyHndrical in shape. Har- 
vesters, printing presses, sewing machines, looms and 
steam-valve mechanisms employ a considerable use 



A PRACTICAL COURSE IN 




^ANGLE OF 
ACT/ON 

Fiff. 132 

of cam constructions, Fig. 132, To draw an involute 
cam with a given rise in a given angle of action, use 
the following: 

Let A = rise of the follower or throw, 

And X = the radius of the base circle C. 

As in the figure, the angle of action is 120 degrees, 

A = % X, % being the ratio of the arc through 



MECHANICAL DRAWING 



129 



LU 




X 




LU 




X 




H 




li. 


tn 


O 


1-4 


h- 


.a" 


z 


h 


UJ 




n 




CL 




O 





> 

UJ 

o 





- (Vi (n 



which the cam works, to a semicircle or straight angle. 

2 = 44/21 X, assuming tt to be 3 1/7. 

X, or the radius, = 2/44/21 = 2x21/44 =1 42/44 
in., or nearly i". 



180 A PRACTICAL COURSE IN 

We assume ^f as being most convenient. With this 
radius draw the base circle C, and construct tangents 
upon which to lay out the involute curve. The ma- 
chine itself will determine the diameter of the disk. 
Lay off the rise of the follower on tangent i, and di- 
vide this into as many parts as tangents have been 
constructed. With center O, draw concentric circles 
to corresponding tangents from the points on the axis 
of the follower (F). 

THE HELIX 

Problem 4. — Fig. 133 shows the development of a 
helical curve as unwrapped from a cylinder. If the 
surface of the cylinder be laid out on paper and a 
diagonal line be draw^n and the paper wrapped about 
the cylinder, the line will then illustrate the helix. 

Problem 5. — The application of the helix may also 
be seen in coil springs, two illustrations of which are 
given. Fig. 134. The constructions may be laid out 
as in Fig. 50, page 52. As in a screw thread the pitch 
of the helix is the distance between two opposite 
points lying on the 'curve and the same cylindrical ele- 
ment. In drawing the spring, use the helical curve as 
a centerline. Draw a number of slnall circles equal 
to the diameter of the round coil desired. The con- 
tour may easily be defined by drawing tangent helices 
to these circles. If square or rectangular material is 
used, draw the helices from each of the four corners, 
A, B, C, D, of the cross section. 

Problem 6, — Make a coil spring from 5" round 
steel, 3!/^" inside diameter, i^'' pitch and 6" long. 

Problem 7. — Make also a square spring out of half- 
inch material, i^'' pitch, 4" outside diameter and 
6" length. 



MECHANICAL DRAWING 



131 



Problem 8. — Determine the length of material re- 
quired in each preceding problem. 




c D 



ff IB 




Fig. 134 



SHEET-METAL PROBLEMS 

On page 91 references were made to the value of 
knowing how to lay out a pattern or template for sheet- 
metal problems. To the sheet-metal draftsman more 
particularly than any other the use of geometric 
methods in drafting is most practical. 

A great many problems of a sheet-metal character 
are, at least, in part warped surfaces. Such surfaces 
are non-developable by any regular method. In the 
development of Fig. 97, the cone is first divided into 
elements of regular intervals, say 12 in all, and their 
true length determined by revolving each fore- 
shortened element parallel to the vertical view. Any 
two true elements laid out with the chord of their 
basal arc will form a triangle. Adjacent triangles are 



132 A PRACTICAL COURSE IN 

constructed in a similar manner and the pattern com- 
pleted. 

Problem p. — Fig. 135 is an illustration of a tran- 
sition piece for a smokestack or blower. Draw to scale 
of i'^ equals I'-o'^ Fig. 136 shows the pattern when 
laid out. 

By observation it will be seen that planes A, B, C, D, 
are triangles whose true shapes can easily be deter- 
mined from the projections. The four corners are 
sections of oblique cones which have been previously 
described. But a shorter method of finding the true 
length of these elements is to find the hypotenuse of 
a right angle the base of which is the distance from 
X or Y in the plan, to points 3, 4, 5 and 6 in the plan. 
The altitude of each triangle is the projected vertical 
altitude as seen in the front view. Lay off the sides 
anywhere as at OP and draw each hypotenuse. These 
are the true lengths desired in the pattern between 
planes A, B, and C. 1"he true lengths of other ele- 
ments are found in a similar way. As the section of 
the top is a circle taken at an angle of 30 deg. from a 
horizontal, an auxiliary view will show a true circle as 
in the front, or top view. A semicircle will suffice. 
Divide into an equal number of points for convenience 
and project back to the corresponding: plan and eleva- 
tion. Connect these points with R, X, Y and Z, and 
proceed with the development. 

Lay off plane A first. Fig. 136. With 6 as a cen- 
ter, strike an arc equal to 6 — 5 (on the section) and 
the pattern with Y as a center and a radius equal to 
5 — 5 at OP. Continue this process until each of the 
longer diagonals are used, half on each side of plane 



MECHANICAL DRAWING 



133 



\2l3^^ 




Fig. 135 



134 



A PRACTICAL COURSE IN 



A. When all of the longer diagonals are used add 
planes B and C, and then add the diagonals laid out 
on the left of OP. The plane D is bisected to show 
a symmetrical development. 




Fig. 136 



Problem lO, — Fig. 137 is the layout and working 
drawing of the base of a smokestack. The top of 
the base is circular in shape while the ends are semi- 
oblique cones.- Make a development of ^ the 
lateral surface similar in shape to Fig. 136, scale i'' 
equals i^-o". 

In this problem it will be necessary to find the true 
length of all elements by revolving the true length (of 
all) parallel to the vertical plane upon which the front 
view is projected. To do this use X' as a center and 



MECHANICAL DRAWING 



135 



X^ — 6 as a radius. Strike an arc upon — X'. Project 
up to the plane AB. Connect the newly found point 
with X and the line will now be seen in its true length 
as it is parallel to V. 




Fig. 137 



When the plane CD cuts the new position, X' — 6 
will be the true length of that portion w^hich consti- 
tutes the surface and can be laid off on X^' — 6 of the 
development. Fig. 138. 



136 



A PRACTICAL COURSE IN 




Fig. 138 



Problem ii, — Fig. 139 is an illustration of a gro- 
cer's scale scoop. 

The development of A is a pattern of the portion 
of a cylinder which a tinsmith would be required to 
lay out for a template. Substitute suitable dimensions 
and draw. Draw a center line X-X to begin. Divide 
the end view of section A into a convenient number of 
similar (equal) parts. Project back to X-X. The 
circumference of section A is next laid out in de- 



MECHANICAL DRAWING 



137 




Fig. 139 



velopment anywhere convenient and the points pro- 
jected to corresponding places. 

SECTIONS OF WORKING DRAWING 

The value of being able to make sections in a draw- 
ing where possible constructive difficulties may arise 
later, is a part of the draftsman's business. Sections 
are very helpful in showing interior constructions and 
in a complicated drawing are absolutely necessary. 
In the illustrations, the sections are shown by cross 
hatching lines, the relation of adjacent parts being 



138 



A PRACTICAL COURSE IN 




Fig. 140 

shown by drawing the hatch Hnes at different angles. 
To determine the location of sections, pass planes 
through the geometric centers of the object, both ver- 
tical and horizontal. On pages 92 and 93 and else- 
where of chapter VIII, sections were made of geomet- 
ric solids and their developments required. Figs. 140 
and 141 are sections of small machine parts and illus- 



— rrr 










^ 


1 


r 

. t 


' — -^ ___^_^^ 




' 7'" 







I ^8 4 




\ 


1 


^ 


[ - - - / 


___— 



Fig. 141 



MECHANICAL DRAWING 



139 



I" 

2 



n 



^^ 





'?^////////////.zA 



^ 



u 



Fig. 142 



trate the practical value of such a construction. Fig. 
142 is a sole plate for a. pillow block. Make freehand 
sketches of each of the sectioned illustrations in order 
to get a pictorial view of the object. 

Problem 12, — On page 67 is an illustration of a 
core box for a pipe tee. 

Fig. 143 is an isometric illustration of a pipe-tee 




Fig. 143 



140 



A PRACTICAL COURSE IN 



pattern but not for the box just referred to. Make 
three views from the illustration, full size. 

Problem is. — Fig. 144 is an illustration of a pat- 
tern for a pedestal bearing. Make three views, g' 

I'-O". 



y 




Fig. 144 



Problem 14. — Fig. 145 is an assembly drawing of 
a simple machine vise. Make a detail drawing filling 
all blank dimensions as indicated in Figs. 146 and 147. 
Those dimensions which are apparently omitted should 



MECHANICAL DRAWING 



Ul 




Fig, 145 



142 



A PRACTICAL COURSE IN 



I 



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i 



3C/?^IV ^O THD3. 



M^ 



o 



TAP/ 



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<OLE 

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1 , 

1 


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t' 

1 


r 

1 


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i' 
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ij. 


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1 


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i j^ 


1 1 


T~ 


1 •— II 


1 1 


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VLL FOR 4 ^/USTER L \ J 
HD. M. SCREW C/. 




t ; 

♦ I 


1 • 1 
1 1 


1 
1 
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1 


































FLATS 



8 THDS P/. SQUARE, LEFT HAND 

1 




vt: — h 

TAP^ ^O THDS. MS. 



^ 



Fig. 146 



MECHANICAL DRAWING 



143 









f 


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~ ~s : 




1 






1 


h-- 






H 


"I 








_ 


>-- 












P , 


J 





^ 








T 
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t ^i__^ 


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1 

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1 


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E 



^-^^ 



DRILLED WHCN IN PO'S/T/ON 
TAP TO FIT SCREW 

-^-^''riLISTER HD. MACH. SCREW 
2 WANTED i"LONG 









^ 



4 WANTED / LONG 



4" ^y^AT HD. MACH. ^C/^EW 4 WANTED 4 LONG 

60: 



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T^ 



DRILL FOR 4 fLAT 
HD. MACH SCREW 



'■i^ 



& 



Fig. 147 



144 A PRACTICAL COURSE IN 

be supplied by the student; but reference should be 
made to the assembly drawing before so doing. Make 
a full-size drawing of the assembled vise before the 
detail drawing. Alake a stock list as suggested on 
page 86. Notes on the detail drawing have reference 
to the work of the machinist in ''finishing" the cast- 
ing after it has been molded from the pattern. Such 
information is essential to a workman and eliminates 
hazardous guesses and mistakes as well as loss of 
time and material. The arrangement of pieces and 
parts should be very carefully planned on the drawing 
paper. In so doing much more can be placed on one 
sheet. 

Problem 15, — Figs. 148 and 149 represent a small 
jack screw in section and detail. Make three views 
and dimension. 

Problem 16. — Fig. 150 is an illustration of Hooke's 
coupling. Three views and section. 

Problem //. — Fig. 151 is a side crank arm. Make 
three views and section at X-x. 

Problem 18. — Fig. 141, page 138, is a turnbuckle. 
Make three views and section. 

Make a drawing of each problem above to scale as 
suggested. Use suitable diameters in each case and 
section. 

Problem 19. — Make an isometric drawing of the 
mission footstool as shown in Fig. 152. 

INTERSECTIONS AND PENETRATIONS 

Problem 20. — The three views of a stub end of a 
connecting rod are shown in Fig. 153. To find the 
curve of intersection, of the cone and prism, pass 
vertical planes A, B, C, D, cutting both the cone and 
rectangular prism. Each plane cuts a circle from the 
cone and a rectangle from the prism. Where these 



MECHANICAL DRAWING 
3'' 



145 




Fig. 148 



146 



A PRACTICAL COURSE IN 



/^ 







^ 



R 



8/' 



OlOOi ' 






'I" 




3 THREADS PER INCH 



Fie. 149 



figures intersect is a point of the curve desired. The 
same method is used in finding a curve of intersection 



MECHANICAL DRAWING 



14' 




Fig. 150 




Fier. 151 



148 



A PRACTICAL COURSE IN 




__- — _(_.__•__ 









18^ 



I 



^le^ 



*2: 



/o 






::d 



"*i^~.r' 

.1 ^ .1. 

I ,1 



-/- 



[f 



I I I 
i._i_. 



L_J 




Fig:. 152 



of a cone and hexagonal prism, or the chamfered por- 
tion of a hexagonal nut. 



MECHANICAL DRAWING 



149 





Fig. 153 



150 A PRACTICAL COURSE IN 

LETTERING EXERCISES 

A great deal of the difficulty which comes to the 
beginner in lettering is due to a vague idea of the 
shape of the individual letter. No draftsman, however 
experienced, can produce well formed letters without 
a clear picture of the shape of each letter and for this 
reason the beginning student should read and follow 
these suggestions closely. Use practice paper, before 
commencing one of the exercises below. 

INSTRUCTIONS 

1. Make the vertical stroke of A, first, then the 
slanting stroke. 

2. Make the bottom part of B wider than the 
upper. 

3. Letters C, G and Q are modifications of the 
letter O. 

4. Keep the bottom part of the letter D full. 

5. The lowest bar of the letter E is a little longer 
than the upper bar. The middle bar is shortest and 
slightly above the center as in F. 

6. Draw the two outside bars of the letter H first. 
Horizontal bar is slightly above center. 

7. The letter J is a portion of the letter U. 

8. Make the short bar of the letter K slope from 
the upper end of the first bar. 

9. Letter M is broad. Draw the two outside bars 
parallel, first, before the intermediate, likewise in the 
letter N. 

10. Letters P and R are similar. Keep the top 
full. 

11. The letter S may best be made inside the letter 
O, with the bottom part a little wider and fuller. 



ALL LETTERS SLOPE HALF THE H/GHT 

^y\\m >o-fn /£^/r^ 

/^m 'L y /^ — ^^ L J L / 




^6 ^ ^2" ■4-5 « 

an/JKL R 
NOFQnB 

/ / ^ I ^ / / 

~U VWK ' 




;t- ^^ 'i 





CARL SCHURZ HIGH 
SCHOOL 

ABCDEFGHIUKLMNOPQR 
STUVWXYZ 



THE QUICK BROWN FOX JUMPS 
OVER THE* LAZY DOG 

Fie. 154 



152 



PENCfL EACH LETTER/NG SHEET ON 
CROSS SECT/ ON RARER RRO\//DED FOR THAT 
RURROSE AND SUBM/T EACH RENC/l^LED 
1./NE TO THE INSTRUCTOR ^OR H/S 
OR/T/C/SM. /N OO/NG TH/S THE STUDENT 
W/l^L. ^A\/E T/ME ANa /MRROVE H/S 
STANDARD OR V^ORKMANSH/R MORE RAR/DLY. 

USE A 2H RENC/L. CON/CAL RO/NT, AL.L. 
DRAW/NGS SHOUi-D BE KERT NEAT AND 
CLEAN. S RACES BET\A/EEM V^ORDS SHALL 
NOT VARY RROM LESS THAN ^ TO MORE 
THAN S D/V/S/ONS ON THE CROSS SECT/ON 
^ARER, SRACES BET\A/EEN RARAGRARHS 
SHOULD BE DOUBLE THE SRACE BET\A/EEN 
1./NES. A S/NGLE SRACE /S SURR/C/ENT 
TO SERARATE L/NES /N THE RARAGRARH. 

INDENT EACH NEW RARAGRARH. USE A 
LARGE RE/\^ BOLDER \A//TH A >3/G ER REN 
RO/NT, HEER THE RENRO/NT CLEAN TO 
ALLOW A STEADY RLO\A/ OR /A/ZT. THE /NK 

CLOGS THE REn's ACT/ON VERY QU/C/<LY. 
DO NOT R/LL the REN RULL OR /N/< /R YOU 
W/SH TO DO EVEN LETTER/r\/G AND AVO/D 
BLOT\S. 

/NDENT 



REPEAT LAST RARAGRARH 



Fig 155 














^; 



1 



K. 



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^^ 



i iiii.ffi[MM)iLr i JHin i >fwi.mH-a 



i / m i ' t ? iw i - t^^ iiz attMa 



a^ 33 ^^ .? >5 ae 77 « a sio. 



/e 

/ 

/6 

/ 

/e 
3 

/6 



/" 


/^' 


3'^ 


/^^ 


5^^ 


3^^ 


7' 


a 


^ 


e 


2 


a 


^ 


a 


/ 
s 


/ 


3 
e 


/ 

2 


a 


3 
-4 


7 
a 


/ 
e 


/ 
4 


3 
a 


/ 

2 


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S 


3 


7 
a 


/6 


7 
/e 




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/a 


/3 
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29 

3a 



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7 

/e 



9 

/© 



// 

/6 



/3 
/6 



/6 



29 
3a 



3 
/6 



5" 
/6 



7 
/6 



16 



If 
16 



13 
16 



15 
16 



29 
32 



32 



3^ 
32 



3 
32 



32 32 

Fig. 156 



/3 
32 



23 
32 



2Q 
32 



MECHANICAL DRAWING 155 

12. Make the first bar of the W slope slightly to 
the right. Keep the letter broad. 

13. Letter V is the letter A upside down. 

14. Widths of all letters are in proportion to their 
heights and should be always so considered. 

15. Common practice among draftsmen employs 
the use of the sloping Gothic letter. Vertical letters 
are commonly used, however, but are more tedious to 
make look well. 

Problem 21. — Make an exercise on >^-in. coordi- 
nate paper of Fig. 154. 

Each small figure pertains to the number of spaces 
upon the section paper. This exercise is a study in 
form and proportion and should be executed with 
much precision and care. Use 2-H pencil, conical 
point. 

Problem 22. — Fig. 155 is an exercise in lettering 
one space high. Herein is the application of the exer- 
cise in Fig. 154. 

Problem 23. — Read the material over carefully and 
apply the directions included therein. Hard practice 
is a good master. Fig. 156 is an exercise of figures 
and fractions on cross-section paper. The draftsman's 
figures are quite different from the commercial figure 
and hence should be scrutinized closely. Fill in all 
vacant spaces and strive for uniformity as in previous 
exercises. 

Problem 24. — Fig. 157 is an exercise in block let- 
tering quite often used in designs for covers, titles, 
headings, etc. Note the divisions of the height are 5 
instead of 8. 



CHAPTER XII 

A SUGGESTED COURSE FOR HIGH SCHOOLS 

Group I. Geometric Exercises 

Problem i. — Bisect a given right line and arc. 

Problem 2, — Erect Is to a given line (any method). 

Problem j. — Draw parallel hnes (two methods). 

Problem 4. — Divide a given line into proportional 
parts. 

Problem 5. — Construct tangents to a given arc of any 
radius. (Fillet.) 

Problem 6. — Duplicate and bisect a given angle. 

Problem 7. — Without triangles construct A. of 30°, 
6o^ 75^ 45^ 22«-30^ 37°-3o'- 

Problem 8. — By triangles only divide a semicircle 
into angles of 15"^. 

Problem p. — Rectify a quadrant of a circle (two 
methods) . Approxmiate. 

Problem 10. — Triangles (trilium — trefoil). 

a. Right angle (rise, run and pitch of a gable roof 
rafter) x^-{-y^ = s^. 

To find the distance across an unknown area — a 
stream, lake or park; also to find altitude of a tree. 

b. Equilateral. (Isometric square — Gothic arch). 

c. Isosceles. 

d. Scalene. 

Query : How find the area of any triangle ? 
What is the sum of all angles of a triangle ? 
Problem 11. Square (bolthead plan — swastika — 
syringa). 

156 



MECHANICAL DRAWING 157 

Problem 12. — Polygons (pansy, violet — crystals). 

a. Pentagon — star (three methods). 

b. Hexagon — bolthead plan (two methods) — star. 

c. Heptagon. 

d. Octagon — taboret top. 

e. Combination of a, b, c, d on a given side of i". 

2n — 4X90 

Prove all polygons by the formula when 

n 

n = the number of sides of polygon. Use the pro- 
tractor to verify. 

Problem /j. — Circles : 

a. Three circles within an equilateral triangle. 

b. Draw circles tangent to each other and the 
given circle, within or without. 

c. Gothic arch. 

d. A circle tangent to a given circle and line. 

e. A circle tangent to two given circles which are 
not tangent to each other. Note : The smallest circle 
is not acceptable. 

*/. A shaft i^" in diameter rotates within a ball- 
bearing consisting of twelve tempered steel balls. 
Make a drawing showing size of balls required. 

g. Four circles within a square. 

//. Maltese cross. 

i. Geometric circular borders. 

j. Moldings — cavetto, cyma, reversa, cyma recta, 
ogee, scotia. 

Problem 14. — Ellipses and elliptic curves (conic sec- 
tions — ecliptic). 

a. Focal method ; circle method. 

b. Trammel method. 

c. Five-point elliptic arch. 



158 A PRACTICAL COURSE IN 

d. Greek, Persian and Gothic arches. 

e. ElHptic cam. 

"^f. The path of a point on a connecting rod in one 
revolution. 
*^. Cycloid. ^ 

*//. Epicycloid. ^ (Gear teeth.) 
i. Hypocycloid. J 

4; Hyperbola. [ (Conic sections.) 
Problem ij, — Spirals : 

a. Archimedean spiral of one or more whorls. 

b. Ionic volute (Ionic capital). 

"^'r. Heart plate cam (sewing-machine bobbin- 
winder). 
"^J. Involute (gear teeth). 
'^c Helix-screw thread, clutch coupling. 

Biographical. — From the encyclopedia read the biog- 
raphies of Archimedes, Pythagoras, Euclid, Vignola. 

It is intended that the number of problems should be 
arranged on the plate according to the local conditions 
of the class-room. Large plates, say 1 5^x20", are 
more comprehensive but require less time for execu- 
tion in proportion to smaller plates. Such problems in 
this outline which have not been given in the text are 
not essential, but, if desired, may be obtained from the 
instructor. Those who expect to study design are not 
required to complete the entire course of mechanical 
drawing. The problems marked by {^) may be 
omitted in this group. 

Group 2. Projections, 

L Working drawings, 

1. Three views of a cylinder. 

2. Three views of a prism. 



MECHANICAL DRAWING 159 

3. Two views of a plinth — one view given 

4. Three views of a pyramid. 

5. Hexagonal nut. 

6. Crank arm. 

7. Small pedestal bearing. 

8. Taboret or stand. 
g: Coat-hanger. 

10. Knife-box. 

11. Tailstock. 

12. Tool-rest. 

Note : The first eight problems are not to be di- 
mensioned. Substitutes may be selected for these 
objects where and when these are not available or 
advisable. Problems 8 to 15 are to be dimensioned 
carefully. Models are to be preferred to a drawing at 
the beginning of this course, so that the absolute rela- 
tion of object to drawing will be established as early as 
possible. 

13. Detailed working drawings from machine parts. 

14. Working drawings from isometric blueprints. 

15. Working drawings from sketches (freehand). 
//. Revolution — Axes of symmetry. 

1. Draw three views of a prism, plinth or pyramid. 

2. Draw three views of No. i when revolved about 
a vertical axis 30°, contra-clockwise. 

3. From No. 2 revolve object about side axis 
through 30° to the left. 

4. From No. i revolve the object forward about a 
front axis 20^. 

5. From No. 2 revolve the object backward about a 
front axis 25°. 

6. From No. 5, 30^ about a side axis, to the right. 

7. From No. 4, 15° about a vertical axis. 

8. From No. 5, 15° to the right about a side axis. 



160 MECHANICAL DRAWING 

Several plates involving the modified positions of 
geometric figures should be drawn that the theory of 
projections may be perfectly clear. Learn the three 
laws of revolution given. 

///. The point J line and plane. (For advanced stu- 
dentSc) Draw in both first and third angles. 

1. Find H and V projections of a point i^^" in 
front of V and 2^" above H. Two inches below" H 
and i^" behind V. Always open the first angle. 

2. Draw the projections of a line which is ^ to the 
H and V planes, 134/' above H and 2" in front of V. 

3. Draw two views of a line oblique to H and /^ 
to V ; oblique to V and ^ to H ; oblique to H and V. 

4. Find the true length of lines in No. 3. What is 
the difference between the projected length and the 
true length of a line ? 

5. Pass a plane (a) / to H; (&) / to V; {c) // 
to P; (d) 1 to H, and any /_ with V; (^) 1 to (V) 
and any /_ with H and P. 

6. Find the intersection of a and £>, also d and c in 5. 

IV, Development of surfaces for patterns of sheet- 
metal and tinsmithing. 
L Parallel lines. Cylinders, prisms, etc. 

2. Radial lines. Cones, pyramids, etc. 

3. Method of triangles. Warped surfaces. 

4. Method of revolution. Frustums and trunca- 
tions. ' 

5. Method of parallel planes ; oblique planes. Pen- 
etrations. 

V\ Penetrations zvith developments included. 
VI. Shades and shadows. 
VII. Mechanical perspective. 



MAR 13 1912 




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